%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO253+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 07:17:43 AM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 4 unt; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 24 ( 7 ~; 7 |; 6 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 21 ( 2 sgn 12 !; 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(a6_defns,axiom,
! [A,L] :
( apart_point_and_line(A,L)
<=> ( right_apart_point(A,L)
| left_apart_point(A,L) ) ),
file('theBenchmark.p',a6_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,B,L] :
( ( incident_point_and_line(B,parallel_through_point(L,A))
& apart_point_and_line(A,L) )
=> apart_point_and_line(B,L) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [A,B,L] :
( ( incident_point_and_line(B,parallel_through_point(L,A))
& apart_point_and_line(A,L) )
=> apart_point_and_line(B,L) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_58,plain,
( right_apart_point(A,B)
| left_apart_point(A,B)
| ~ apart_point_and_line(A,B) ),
inference(clausify,[status(thm)],[a6_defns]) ).
fof(nnf_37,plain,
? [A,B,L] :
( ~ apart_point_and_line(B,L)
& incident_point_and_line(B,parallel_through_point(L,A))
& apart_point_and_line(A,L) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ apart_point_and_line(sK2,sK1)
& incident_point_and_line(sK2,parallel_through_point(sK1,sK0))
& apart_point_and_line(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(B,sK2),skolemize(L,sK1)],[nnf_37]) ).
cnf(c_65,negated_conjecture,
apart_point_and_line(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_78,negated_conjecture,
( right_apart_point(sK0,sK1)
| left_apart_point(sK0,sK1) ),
inference(resolve,[status(thm)],[c_65,c_58]) ).
cnf(c_86,plain,
( left_apart_point(A,reverse_line(B))
| ~ right_apart_point(A,B) ),
inference(clausify,[status(thm)],[a2_defns]) ).
cnf(c_102,negated_conjecture,
( left_apart_point(sK0,sK1)
| left_apart_point(sK0,reverse_line(sK1)) ),
inference(resolve,[status(thm)],[c_86,c_78]) ).
cnf(c_118,plain,
~ left_apart_point(A,B),
inference(clausify,[status(thm)],[ax10_basics]) ).
cnf(c_136,negated_conjecture,
left_apart_point(sK0,sK1),
inference(resolve,[status(thm)],[c_118,c_102]) ).
cnf(c_135,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_118,c_136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO253+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n004.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 13:10:35 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 3239589 was started by sandbox on n004,
% 0.09/0.36 % Fri Sep 25 13:10:35 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/0.37
% 0.13/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 11.
% 0.13/0.38 % Level of proof is 4.
% 0.13/0.38 % Maximum clause weight is 7.000.
% 0.13/0.38 % Given clauses 0.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------