%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO252+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 : 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 07:17:42 AM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% 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 : 5 ( 5 usr; 3 con; 0-2 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,B,L] :
( ( right_apart_point(B,L)
& left_apart_point(A,L) )
=> ( left_convergent_lines(line_connecting(A,B),L)
& distinct_points(A,B) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [A,B,L] :
( ( right_apart_point(B,L)
& left_apart_point(A,L) )
=> ( left_convergent_lines(line_connecting(A,B),L)
& distinct_points(A,B) ) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(nnf_37,plain,
? [A,B,L] :
( ( ~ left_convergent_lines(line_connecting(A,B),L)
| ~ distinct_points(A,B) )
& right_apart_point(B,L)
& left_apart_point(A,L) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ( ~ left_convergent_lines(line_connecting(sK2,sK0),sK1)
| ~ distinct_points(sK2,sK0) )
& right_apart_point(sK0,sK1)
& left_apart_point(sK2,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK1,sK0]),skolemize(A,sK2),skolemize(B,sK0),skolemize(L,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
% 0.00/0.03 % Problem : GEO252+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n002.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 13:13:19 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.37 % Process 3348463 was started by sandbox on n002,
% 0.08/0.37 % Fri Sep 25 13:13:19 2026
% 0.08/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.38
% 0.08/0.38 % From the command line: assign(max_seconds, 300).
% 0.14/0.39
% 0.14/0.39 % SZS status Theorem for theBenchmark
% 0.14/0.39
% 0.14/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.14/0.39 % Length of proof is 8.
% 0.14/0.39 % Level of proof is 3.
% 0.14/0.39 % Maximum clause weight is 4.000.
% 0.14/0.39 % Given clauses 0.
% 0.14/0.39
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------