%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN398+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 09:37:48 AM UTC 2026
% Result : Theorem 0.09s 0.38s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 4 unt; 0 def)
% Number of atoms : 41 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 47 ( 18 ~; 15 |; 12 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 2 prp; 0-1 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 15 ( 3 sgn 10 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(kalish215,conjecture,
( ! [X] :
( f(X)
& p )
<=> ( ! [Y] : f(Y)
& p ) ),
file('theBenchmark.p',kalish215) ).
fof(kalish215_neg,negated_conjecture,
~ ( ! [X] :
( f(X)
& p )
<=> ( ! [Y] : f(Y)
& p ) ),
inference(assume_negation,[status(cth)],[kalish215]) ).
fof(nnf_1,plain,
( ( ? [Y] : ~ f(Y)
| ~ p
| ? [X] :
( ~ f(X)
| ~ p ) )
& ( ( ! [X1] : f(X1)
& p )
| ! [X0] :
( f(X0)
& p ) ) ),
inference(fof_nnf,[status(thm)],[kalish215_neg]) ).
fof(sk_kalish215_neg_sk,plain,
( ( ~ f(sK1)
| ~ p
| ~ f(sK0)
| ~ p )
& ( ( ! [X1] : f(X1)
& p )
| ! [X0] :
( f(X0)
& p ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(Y,sK1)],[nnf_1]) ).
fof(sk_kalish215_neg,plain,
( ( ~ f(sK1)
| ~ f(sK0)
| ~ p )
& ! [VAR_0,VAR_1] :
( f(VAR_1)
| f(VAR_0) )
& p ),
inference(cnf_transformation,[status(thm)],[sk_kalish215_neg_sk]) ).
cnf(c_2,negated_conjecture,
p,
inference(split_conjunct,[status(thm)],[sk_kalish215_neg]) ).
cnf(c_3,negated_conjecture,
( f(B)
| f(A) ),
inference(split_conjunct,[status(thm)],[sk_kalish215_neg]) ).
cnf(c_4,negated_conjecture,
( ~ f(sK1)
| ~ f(sK0)
| ~ p ),
inference(split_conjunct,[status(thm)],[sk_kalish215_neg]) ).
cnf(c_5,negated_conjecture,
( ~ f(sK1)
| ~ f(sK0) ),
inference(resolve,[status(thm)],[c_2,c_4]) ).
cnf(c_6,plain,
f(A),
inference(factor,[status(thm)],[c_3]) ).
cnf(c_8,negated_conjecture,
~ f(sK1),
inference(resolve,[status(thm)],[c_6,c_5]) ).
cnf(c_7,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_6,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN398+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 17:41:34 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2145580 was started by sandbox on n020,
% 0.09/0.37 % Sat Sep 26 17:41:34 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.38
% 0.09/0.38 % SZS status Theorem for theBenchmark
% 0.09/0.38
% 0.09/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.38 % Length of proof is 7.
% 0.09/0.38 % Level of proof is 3.
% 0.09/0.38 % Maximum clause weight is 4.000.
% 0.09/0.38 % Given clauses 0.
% 0.09/0.38
% 0.09/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------