%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV011+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 09:06:38 AM UTC 2026
% Result : Theorem 0.15s 0.44s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 9 ( 6 unt; 0 def)
% Number of atoms : 12 ( 0 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 4 ~; 1 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 3 ( 0 sgn 0 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(co1,conjecture,
? [U] :
( b_holds(key(U,a))
& a_holds(key(U,b)) ),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ ? [U] :
( b_holds(key(U,a))
& a_holds(key(U,b)) ),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_2,negated_conjecture,
( ~ b_holds(key(A,a))
| ~ a_holds(key(A,b)) ),
inference(clausify,[status(thm)],[co1_neg]) ).
fof(ax3,axiom,
a_holds(key(generate_key(an_a_nonce),b)),
file('theBenchmark.p',ax3) ).
cnf(c_3,plain,
a_holds(key(generate_key(an_a_nonce),b)),
inference(clausify,[status(thm)],[ax3]) ).
cnf(c_5,negated_conjecture,
~ b_holds(key(generate_key(an_a_nonce),a)),
inference(resolve,[status(thm)],[c_2,c_3]) ).
fof(ax1,axiom,
b_holds(key(generate_key(an_a_nonce),a)),
file('theBenchmark.p',ax1) ).
cnf(c_6,plain,
b_holds(key(generate_key(an_a_nonce),a)),
inference(clausify,[status(thm)],[ax1]) ).
cnf(c_8,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_5,c_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV011+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.41 % Computer : n011.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.42 % WCLimit : 300
% 0.15/0.42 % DateTime : Sat Sep 26 13:05:31 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.42 % Process 612056 was started by sandbox2 on n011,
% 0.15/0.42 % Sat Sep 26 13:05:31 2026
% 0.15/0.42 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.43
% 0.15/0.43 % From the command line: assign(max_seconds, 300).
% 0.15/0.44
% 0.15/0.44 % SZS status Theorem for theBenchmark
% 0.15/0.44
% 0.15/0.44 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/0.44 % Length of proof is 6.
% 0.15/0.44 % Level of proof is 3.
% 0.15/0.44 % Maximum clause weight is 0.000.
% 0.15/0.44 % Given clauses 0.
% 0.15/0.44
% 0.15/0.44 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------