%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN959+1 : TPTP v9.3.1. Released v3.1.0.
% 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 09:43:27 AM UTC 2026
% Result : Theorem 0.16s 0.40s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1
% Syntax : Number of formulae : 7 ( 3 unt; 0 def)
% Number of atoms : 15 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 14 ( 6 ~; 2 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 1 ( 1 usr; 1 con; 0-0 aty)
% Number of variables : 8 ( 1 sgn 2 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
( ? [X] : b(X)
=> ? [X] :
( b(X)
| a(X) ) ),
file('theBenchmark.p',prove_this) ).
fof(prove_this_neg,negated_conjecture,
~ ( ? [X] : b(X)
=> ? [X] :
( b(X)
| a(X) ) ),
inference(assume_negation,[status(cth)],[prove_this]) ).
fof(nnf_1,plain,
( ! [X] :
( ~ b(X)
& ~ a(X) )
& ? [X0] : b(X0) ),
inference(fof_nnf,[status(thm)],[prove_this_neg]) ).
fof(sk_prove_this_neg,plain,
( ! [X] :
( ~ b(X)
& ~ a(X) )
& b(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_1]) ).
cnf(c_2,negated_conjecture,
~ b(A),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_3,negated_conjecture,
b(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_this_neg]) ).
cnf(c_4,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2,c_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYN959+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 18:49:54 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.39 % Process 238428 was started by sandbox on n007,
% 0.11/0.39 % Sat Sep 26 18:49:54 2026
% 0.11/0.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.40
% 0.11/0.40 % From the command line: assign(max_seconds, 300).
% 0.16/0.40
% 0.16/0.40 % SZS status Theorem for theBenchmark
% 0.16/0.40
% 0.16/0.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/0.40 % Length of proof is 4.
% 0.16/0.40 % Level of proof is 2.
% 0.16/0.40 % Maximum clause weight is 0.000.
% 0.16/0.40 % Given clauses 0.
% 0.16/0.40
% 0.16/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------