%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL648+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 07:59:18 AM UTC 2026
% Result : Theorem 0.16s 0.38s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 11 ( 5 unt; 0 def)
% Number of atoms : 34 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 50 ( 27 ~; 13 |; 10 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 11 ( 0 sgn 6 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(main,conjecture,
~ ? [X] :
~ ( ! [Y] :
( ~ ( p101(Y)
& p201(Y) )
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( p101(Y)
& p201(Y) )
| ~ r1(X,Y) ) ),
file('theBenchmark.p',main) ).
fof(main_neg,negated_conjecture,
~ ~ ? [X] :
~ ( ! [Y] :
( ~ ( p101(Y)
& p201(Y) )
| ~ r1(X,Y) )
| ~ ! [Y] :
( ~ ( p101(Y)
& p201(Y) )
| ~ r1(X,Y) ) ),
inference(assume_negation,[status(cth)],[main]) ).
fof(nnf_1,plain,
? [X] :
( ? [Y] :
( p101(Y)
& p201(Y)
& r1(X,Y) )
& ! [X0] :
( ~ p101(X0)
| ~ p201(X0)
| ~ r1(X,X0) ) ),
inference(fof_nnf,[status(thm)],[main_neg]) ).
fof(sk_main_neg,plain,
( p101(sK1)
& p201(sK1)
& r1(sK0,sK1)
& ! [X0] :
( ~ p101(X0)
| ~ p201(X0)
| ~ r1(sK0,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_1]) ).
cnf(c_2,negated_conjecture,
r1(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_3,negated_conjecture,
( ~ p101(A)
| ~ p201(A)
| ~ r1(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_4,negated_conjecture,
p201(sK1),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_5,negated_conjecture,
( ~ p101(sK1)
| ~ p201(sK1) ),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_6,negated_conjecture,
p101(sK1),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_7,negated_conjecture,
~ p101(sK1),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_8,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_6,c_7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL648+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36 % Computer : n003.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Fri Sep 25 22:57:52 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.16/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.36 % Process 1344482 was started by sandbox2 on n003,
% 0.16/0.36 % Fri Sep 25 22:57:52 2026
% 0.16/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.37
% 0.16/0.37 % From the command line: assign(max_seconds, 300).
% 0.16/0.38
% 0.16/0.38 % SZS status Theorem for theBenchmark
% 0.16/0.38
% 0.16/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/0.38 % Length of proof is 8.
% 0.16/0.38 % Level of proof is 4.
% 0.16/0.38 % Maximum clause weight is 0.000.
% 0.16/0.38 % Given clauses 0.
% 0.16/0.38
% 0.16/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------