%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN399+1 : TPTP v9.3.1. Released v2.0.0.
% 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 09:37:48 AM UTC 2026
% Result : Theorem 0.15s 0.38s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 1
% Syntax : Number of formulae : 14 ( 3 unt; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 53 ( 20 ~; 18 |; 9 &)
% ( 4 <=>; 2 =>; 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 : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 15 ( 3 sgn 11 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(kalish223,conjecture,
( ! [X] :
( f(X)
<=> p )
=> ( ! [Y] : f(Y)
<=> p ) ),
file('theBenchmark.p',kalish223) ).
fof(kalish223_neg,negated_conjecture,
~ ( ! [X] :
( f(X)
<=> p )
=> ( ! [Y] : f(Y)
<=> p ) ),
inference(assume_negation,[status(cth)],[kalish223]) ).
fof(nnf_1,plain,
( ( ~ p
| ? [Y] : ~ f(Y) )
& ( p
| ! [X0] : f(X0) )
& ! [X] :
( ( ~ p
| f(X) )
& ( p
| ~ f(X) ) ) ),
inference(fof_nnf,[status(thm)],[kalish223_neg]) ).
fof(sk_kalish223_neg_sk,plain,
( ( ~ p
| ~ f(sK0) )
& ( p
| ! [X0] : f(X0) )
& ! [X] :
( ( ~ p
| f(X) )
& ( p
| ~ f(X) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Y,sK0)],[nnf_1]) ).
fof(sk_kalish223_neg,plain,
( ( ~ p
| ~ f(sK0) )
& ! [VAR_0] :
( p
| f(VAR_0) )
& ! [VAR_0] :
( ~ p
| f(VAR_0) )
& ! [VAR_0] :
( p
| ~ f(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_kalish223_neg_sk]) ).
cnf(c_2,negated_conjecture,
( ~ p
| f(A) ),
inference(split_conjunct,[status(thm)],[sk_kalish223_neg]) ).
cnf(c_3,negated_conjecture,
( p
| ~ f(A) ),
inference(split_conjunct,[status(thm)],[sk_kalish223_neg]) ).
cnf(c_4,negated_conjecture,
( p
| f(A) ),
inference(split_conjunct,[status(thm)],[sk_kalish223_neg]) ).
cnf(c_5,negated_conjecture,
( ~ p
| ~ f(sK0) ),
inference(split_conjunct,[status(thm)],[sk_kalish223_neg]) ).
cnf(c_6,negated_conjecture,
( ~ p
| ~ p ),
inference(resolve,[status(thm)],[c_5,c_2]) ).
cnf(c_7,negated_conjecture,
~ p,
inference(copy,[status(thm)],[c_6]) ).
cnf(c_8,negated_conjecture,
( p
| p ),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_10,negated_conjecture,
p,
inference(copy,[status(thm)],[c_8]) ).
cnf(c_9,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_7,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN399+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n005.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 17:40:32 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.37 % Process 2676135 was started by sandbox2 on n005,
% 0.12/0.37 % Sat Sep 26 17:40:32 2026
% 0.12/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.38
% 0.15/0.38 % From the command line: assign(max_seconds, 300).
% 0.15/0.38
% 0.15/0.38 % SZS status Theorem for theBenchmark
% 0.15/0.38
% 0.15/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/0.38 % Length of proof is 9.
% 0.15/0.38 % Level of proof is 4.
% 0.15/0.38 % Maximum clause weight is 1.000.
% 0.15/0.38 % Given clauses 0.
% 0.15/0.38
% 0.15/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------