%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO206+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 07:17:28 AM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 10 unt; 0 def)
% Number of atoms : 43 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 43 ( 21 ~; 12 |; 6 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 33 ( 3 sgn 16 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('theBenchmark.p',apart6) ).
fof(cp1,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('theBenchmark.p',cp1) ).
fof(cp2,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('theBenchmark.p',cp2) ).
fof(cup1,axiom,
! [X,Y,Z] :
( distinct_lines(Y,Z)
=> ( convergent_lines(Y,Z)
| apart_point_and_line(X,Z)
| apart_point_and_line(X,Y) ) ),
file('theBenchmark.p',cup1) ).
fof(con,conjecture,
! [X,Y,Z] :
( ( ~ convergent_lines(Y,Z)
& ~ apart_point_and_line(X,Y) )
=> ~ distinct_lines(Y,parallel_through_point(Z,X)) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ convergent_lines(Y,Z)
& ~ apart_point_and_line(X,Y) )
=> ~ distinct_lines(Y,parallel_through_point(Z,X)) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_22,plain,
( convergent_lines(B,C)
| convergent_lines(A,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[apart6]) ).
cnf(c_31,plain,
~ convergent_lines(parallel_through_point(A,B),A),
inference(clausify,[status(thm)],[cp1]) ).
cnf(c_32,plain,
~ apart_point_and_line(A,parallel_through_point(B,A)),
inference(clausify,[status(thm)],[cp2]) ).
cnf(c_33,plain,
( convergent_lines(A,B)
| apart_point_and_line(C,B)
| apart_point_and_line(C,A)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[cup1]) ).
fof(nnf_16,plain,
? [X,Y,Z] :
( distinct_lines(Y,parallel_through_point(Z,X))
& ~ convergent_lines(Y,Z)
& ~ apart_point_and_line(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( distinct_lines(sK1,parallel_through_point(sK2,sK0))
& ~ convergent_lines(sK1,sK2)
& ~ apart_point_and_line(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X,sK0),skolemize(Y,sK1),skolemize(Z,sK2)],[nnf_16]) ).
cnf(c_34,negated_conjecture,
~ apart_point_and_line(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_35,negated_conjecture,
~ convergent_lines(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_36,negated_conjecture,
distinct_lines(sK1,parallel_through_point(sK2,sK0)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_58,negated_conjecture,
( convergent_lines(A,sK2)
| ~ convergent_lines(sK1,A) ),
inference(resolve,[status(thm)],[c_22,c_35]) ).
cnf(c_43,negated_conjecture,
~ convergent_lines(sK1,parallel_through_point(sK2,A)),
inference(resolve,[status(thm)],[c_58,c_31]) ).
cnf(c_59,negated_conjecture,
( convergent_lines(sK1,parallel_through_point(sK2,sK0))
| apart_point_and_line(A,parallel_through_point(sK2,sK0))
| apart_point_and_line(A,sK1) ),
inference(resolve,[status(thm)],[c_36,c_33]) ).
cnf(c_44,negated_conjecture,
( apart_point_and_line(A,parallel_through_point(sK2,sK0))
| apart_point_and_line(A,sK1) ),
inference(resolve,[status(thm)],[c_43,c_59]) ).
cnf(c_60,plain,
apart_point_and_line(sK0,sK1),
inference(resolve,[status(thm)],[c_44,c_32]) ).
cnf(c_57,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_34,c_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO206+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n026.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Fri Sep 25 13:08:40 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 2587153 was started by sandbox2 on n026,
% 0.17/0.43 % Fri Sep 25 13:08:40 2026
% 0.17/0.43 % 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).
% 0.17/0.46
% 0.17/0.46 % SZS status Theorem for theBenchmark
% 0.17/0.46
% 0.17/0.46 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.46 % Length of proof is 15.
% 0.17/0.46 % Level of proof is 4.
% 0.17/0.46 % Maximum clause weight is 12.000.
% 0.17/0.46 % Given clauses 26.
% 0.17/0.46
% 0.17/0.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------