%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL684+1.001 : 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 : n012.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 07:59:31 AM UTC 2026
% Result : Theorem 0.04s 0.32s
% Output : CNFRefutation 0.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 2
% Syntax : Number of formulae : 14 ( 6 unt; 0 def)
% Number of atoms : 45 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 68 ( 37 ~; 21 |; 10 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 19 ( 0 sgn 11 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity,axiom,
! [X] : r1(X,X),
file('theBenchmark.p',reflexivity) ).
fof(main,conjecture,
~ ? [X] :
~ ( ~ ( p101(X)
& p201(X) )
| ~ ! [Y] :
( ! [X] :
( ~ ( p101(X)
& p201(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) ),
file('theBenchmark.p',main) ).
fof(main_neg,negated_conjecture,
~ ~ ? [X] :
~ ( ~ ( p101(X)
& p201(X) )
| ~ ! [Y] :
( ! [X] :
( ~ ( p101(X)
& p201(X) )
| ~ r1(Y,X) )
| ~ r1(X,Y) ) ),
inference(assume_negation,[status(cth)],[main]) ).
fof(nnf_3,plain,
? [X] :
( p101(X)
& p201(X)
& ! [Y] :
( ! [X0] :
( ~ p101(X0)
| ~ p201(X0)
| ~ r1(Y,X0) )
| ~ r1(X,Y) ) ),
inference(fof_nnf,[status(thm)],[main_neg]) ).
fof(sk_main_neg_sk,plain,
( p101(sK0)
& p201(sK0)
& ! [Y] :
( ! [X0] :
( ~ p101(X0)
| ~ p201(X0)
| ~ r1(Y,X0) )
| ~ r1(sK0,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X,sK0)],[nnf_3]) ).
fof(sk_main_neg,plain,
( p101(sK0)
& p201(sK0)
& ! [VAR_0,VAR_1] :
( ~ p101(VAR_1)
| ~ p201(VAR_1)
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_main_neg_sk]) ).
cnf(c_4,negated_conjecture,
p201(sK0),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_5,negated_conjecture,
( ~ p101(B)
| ~ p201(B)
| ~ r1(A,B)
| ~ r1(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_6,negated_conjecture,
p101(sK0),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_7,negated_conjecture,
( ~ p101(sK0)
| ~ r1(A,sK0)
| ~ r1(sK0,A) ),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_8,negated_conjecture,
( ~ r1(A,sK0)
| ~ r1(sK0,A) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_9,plain,
r1(A,A),
inference(clausify,[status(thm)],[reflexivity]) ).
cnf(c_12,negated_conjecture,
~ r1(sK0,sK0),
inference(resolve,[status(thm)],[c_9,c_8]) ).
cnf(c_11,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_9,c_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : LCL684+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Fri Sep 25 23:21:06 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.04/0.30 % Process 3301388 was started by sandbox on n012,
% 0.04/0.30 % Fri Sep 25 23:21:06 2026
% 0.04/0.30 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.04/0.30
% 0.04/0.30 % From the command line: assign(max_seconds, 300).
% 0.04/0.32
% 0.04/0.32 % SZS status Theorem for theBenchmark
% 0.04/0.32
% 0.04/0.32 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.04/0.32 % Length of proof is 9.
% 0.04/0.32 % Level of proof is 4.
% 0.04/0.32 % Maximum clause weight is 6.000.
% 0.04/0.32 % Given clauses 2.
% 0.04/0.32
% 0.04/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------