%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN406+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 : n007.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 0.16s 0.43s
% 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 : 33 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 33 ( 11 ~; 6 |; 12 &)
% ( 0 <=>; 4 =>; 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 6 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(kalish240,conjecture,
( ( ? [Y] :
( h(Y)
& f(Y) )
& ! [X] :
( f(X)
=> g(X) ) )
=> ? [Z] :
( h(Z)
& g(Z) ) ),
file('theBenchmark.p',kalish240) ).
fof(kalish240_neg,negated_conjecture,
~ ( ( ? [Y] :
( h(Y)
& f(Y) )
& ! [X] :
( f(X)
=> g(X) ) )
=> ? [Z] :
( h(Z)
& g(Z) ) ),
inference(assume_negation,[status(cth)],[kalish240]) ).
fof(nnf_1,plain,
( ! [Z] :
( ~ h(Z)
| ~ g(Z) )
& ? [Y] :
( h(Y)
& f(Y) )
& ! [X] :
( g(X)
| ~ f(X) ) ),
inference(fof_nnf,[status(thm)],[kalish240_neg]) ).
fof(sk_kalish240_neg,plain,
( ! [Z] :
( ~ h(Z)
| ~ g(Z) )
& h(sK0)
& f(sK0)
& ! [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_kalish240_neg]) ).
cnf(c_3,negated_conjecture,
( g(A)
| ~ f(A) ),
inference(split_conjunct,[status(thm)],[sk_kalish240_neg]) ).
cnf(c_4,negated_conjecture,
( ~ h(A)
| ~ g(A) ),
inference(split_conjunct,[status(thm)],[sk_kalish240_neg]) ).
cnf(c_5,negated_conjecture,
g(sK0),
inference(resolve,[status(thm)],[c_2,c_3]) ).
cnf(c_6,negated_conjecture,
h(sK0),
inference(split_conjunct,[status(thm)],[sk_kalish240_neg]) ).
cnf(c_7,negated_conjecture,
~ h(sK0),
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
% 0.00/0.04 % Problem : SYN406+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.41 % Computer : n007.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 17:38:54 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.42 % Process 108376 was started by sandbox on n007,
% 0.16/0.42 % Sat Sep 26 17:38:54 2026
% 0.16/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/0.43
% 0.16/0.43 % From the command line: assign(max_seconds, 300).
% 0.16/0.43
% 0.16/0.43 % SZS status Theorem for theBenchmark
% 0.16/0.43
% 0.16/0.43 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/0.43 % Length of proof is 8.
% 0.16/0.43 % Level of proof is 4.
% 0.16/0.43 % Maximum clause weight is 0.000.
% 0.16/0.43 % Given clauses 0.
% 0.16/0.43
% 0.16/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------