%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO171+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 : n017.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 07:17:14 AM UTC 2026
% Result : Theorem 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 17 ( 7 unt; 0 def)
% Number of atoms : 31 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 12 ~; 8 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 23 ( 0 sgn 11 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X),
file('theBenchmark.p',apart3) ).
fof(ax6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('theBenchmark.p',ax6) ).
fof(ceq3,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('theBenchmark.p',ceq3) ).
fof(con,conjecture,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(nnf_36,plain,
? [X,Y] :
( ~ distinct_lines(X,Y)
& convergent_lines(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ distinct_lines(sK0,sK1)
& convergent_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_36]) ).
cnf(c_47,negated_conjecture,
~ distinct_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_48,negated_conjecture,
convergent_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_69,plain,
( convergent_lines(A,C)
| distinct_lines(B,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ceq3]) ).
cnf(c_77,plain,
( convergent_lines(B,C)
| convergent_lines(A,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ax6]) ).
cnf(c_80,plain,
~ convergent_lines(A,A),
inference(clausify,[status(thm)],[apart3]) ).
cnf(c_112,negated_conjecture,
( convergent_lines(A,sK1)
| ~ convergent_lines(A,sK0) ),
inference(resolve,[status(thm)],[c_69,c_47]) ).
cnf(c_100,negated_conjecture,
~ convergent_lines(sK1,sK0),
inference(resolve,[status(thm)],[c_112,c_80]) ).
cnf(c_113,plain,
( convergent_lines(B,A)
| ~ convergent_lines(A,B) ),
inference(resolve,[status(thm)],[c_77,c_80]) ).
cnf(c_114,plain,
~ convergent_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_113,c_100]) ).
cnf(c_111,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_48,c_114]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO171+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n017.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 12:56:18 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.38 % Process 2318025 was started by sandbox on n017,
% 0.10/0.38 % Fri Sep 25 12:56:18 2026
% 0.10/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.10/0.40
% 0.10/0.40 % SZS status Theorem for theBenchmark
% 0.10/0.40
% 0.10/0.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.40 % Length of proof is 11.
% 0.10/0.40 % Level of proof is 3.
% 0.10/0.40 % Maximum clause weight is 14.000.
% 0.10/0.40 % Given clauses 38.
% 0.10/0.40
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------