%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN407+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 : n001.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 09:37:49 AM UTC 2026
% Result : Theorem 0.19s 0.48s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 42 ( 14 ~; 14 |; 8 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 13 ( 0 sgn 8 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(kalish241,conjecture,
( ! [X] :
( f(X)
=> ( h(X)
| g(X) ) )
=> ( ? [Z] :
( h(Z)
& f(Z) )
| ! [Y] :
( f(Y)
=> g(Y) ) ) ),
file('theBenchmark.p',kalish241) ).
fof(kalish241_neg,negated_conjecture,
~ ( ! [X] :
( f(X)
=> ( h(X)
| g(X) ) )
=> ( ? [Z] :
( h(Z)
& f(Z) )
| ! [Y] :
( f(Y)
=> g(Y) ) ) ),
inference(assume_negation,[status(cth)],[kalish241]) ).
fof(nnf_1,plain,
( ! [Z] :
( ~ h(Z)
| ~ f(Z) )
& ? [Y] :
( ~ g(Y)
& f(Y) )
& ! [X] :
( h(X)
| g(X)
| ~ f(X) ) ),
inference(fof_nnf,[status(thm)],[kalish241_neg]) ).
fof(sk_kalish241_neg,plain,
( ! [Z] :
( ~ h(Z)
| ~ f(Z) )
& ~ g(sK0)
& f(sK0)
& ! [X] :
( h(X)
| g(X)
| ~ f(X) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Y,sK0)],[nnf_1]) ).
cnf(c_2,negated_conjecture,
f(sK0),
inference(split_conjunct,[status(thm)],[sk_kalish241_neg]) ).
cnf(c_3,negated_conjecture,
( h(A)
| g(A)
| ~ f(A) ),
inference(split_conjunct,[status(thm)],[sk_kalish241_neg]) ).
cnf(c_4,negated_conjecture,
( ~ h(A)
| ~ f(A) ),
inference(split_conjunct,[status(thm)],[sk_kalish241_neg]) ).
cnf(c_5,negated_conjecture,
~ g(sK0),
inference(split_conjunct,[status(thm)],[sk_kalish241_neg]) ).
cnf(c_6,negated_conjecture,
( h(sK0)
| g(sK0) ),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_7,negated_conjecture,
~ h(sK0),
inference(resolve,[status(thm)],[c_4,c_2]) ).
cnf(c_8,negated_conjecture,
h(sK0),
inference(resolve,[status(thm)],[c_5,c_6]) ).
cnf(c_9,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_7,c_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SYN407+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n001.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 17:46:44 UTC 2026
% 0.19/0.46 % CPUTime :
% 0.19/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.46 % Process 2352705 was started by sandbox on n001,
% 0.19/0.46 % Sat Sep 26 17:46:44 2026
% 0.19/0.46 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/0.47
% 0.19/0.47 % From the command line: assign(max_seconds, 300).
% 0.19/0.48
% 0.19/0.48 % SZS status Theorem for theBenchmark
% 0.19/0.48
% 0.19/0.48 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.19/0.48 % Length of proof is 9.
% 0.19/0.48 % Level of proof is 4.
% 0.19/0.48 % Maximum clause weight is 0.000.
% 0.19/0.48 % Given clauses 0.
% 0.19/0.48
% 0.19/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------