%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO217+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 : n005.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 07:17:32 AM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 9 unt; 0 def)
% Number of atoms : 33 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 37 ( 22 ~; 6 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 22 ( 0 sgn 10 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X),
file('theBenchmark.p',apart3) ).
fof(apart6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('theBenchmark.p',apart6) ).
fof(con,conjecture,
! [L,M,N] :
( ( ~ convergent_lines(L,N)
& ~ convergent_lines(L,M) )
=> ~ convergent_lines(M,N) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [L,M,N] :
( ( ~ convergent_lines(L,N)
& ~ convergent_lines(L,M) )
=> ~ convergent_lines(M,N) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_19,plain,
~ convergent_lines(A,A),
inference(clausify,[status(thm)],[apart3]) ).
cnf(c_22,plain,
( convergent_lines(B,C)
| convergent_lines(A,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[apart6]) ).
fof(nnf_16,plain,
? [L,M,N] :
( convergent_lines(M,N)
& ~ convergent_lines(L,N)
& ~ convergent_lines(L,M) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( convergent_lines(sK1,sK2)
& ~ convergent_lines(sK0,sK2)
& ~ convergent_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(L,sK0),skolemize(M,sK1),skolemize(N,sK2)],[nnf_16]) ).
cnf(c_37,negated_conjecture,
~ convergent_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_38,negated_conjecture,
~ convergent_lines(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_39,negated_conjecture,
convergent_lines(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_49,plain,
( convergent_lines(B,A)
| ~ convergent_lines(A,B) ),
inference(resolve,[status(thm)],[c_22,c_19]) ).
cnf(c_40,negated_conjecture,
~ convergent_lines(sK1,sK0),
inference(resolve,[status(thm)],[c_49,c_37]) ).
cnf(c_50,plain,
( convergent_lines(B,A)
| ~ convergent_lines(A,B) ),
inference(resolve,[status(thm)],[c_22,c_19]) ).
cnf(c_41,negated_conjecture,
~ convergent_lines(sK2,sK0),
inference(resolve,[status(thm)],[c_50,c_38]) ).
cnf(c_51,plain,
( convergent_lines(A,sK0)
| ~ convergent_lines(sK1,A) ),
inference(resolve,[status(thm)],[c_22,c_40]) ).
cnf(c_52,plain,
~ convergent_lines(sK1,sK2),
inference(resolve,[status(thm)],[c_51,c_41]) ).
cnf(c_48,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_39,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO217+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n005.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 13:07:17 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 3547342 was started by sandbox2 on n005,
% 0.10/0.36 % Fri Sep 25 13:07:17 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.39
% 0.13/0.39 % SZS status Theorem for theBenchmark
% 0.13/0.39
% 0.13/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.39 % Length of proof is 11.
% 0.13/0.39 % Level of proof is 3.
% 0.13/0.39 % Maximum clause weight is 9.000.
% 0.13/0.39 % Given clauses 24.
% 0.13/0.39
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------