%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SYN722+1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n003.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 09:39:12 AM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 4 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 10 ( 4 avg)
% Number of connectives : 87 ( 40 ~; 35 |; 12 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-1 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 17 ( 4 sgn 8 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thm119,conjecture,
~ ( ( ~ p(b)
| ~ p(a) )
& ! [X] :
? [Y] :
( ~ q(d)
| ~ q(c)
| ~ q(Y)
| ~ q(X)
| p(X) )
& ! [Z] :
( q(Z)
& ( r(Z)
| p(Z) ) ) ),
file('theBenchmark.p',thm119) ).
fof(thm119_neg,negated_conjecture,
~ ~ ( ( ~ p(b)
| ~ p(a) )
& ! [X] :
? [Y] :
( ~ q(d)
| ~ q(c)
| ~ q(Y)
| ~ q(X)
| p(X) )
& ! [Z] :
( q(Z)
& ( r(Z)
| p(Z) ) ) ),
inference(assume_negation,[status(cth)],[thm119]) ).
fof(nnf_1,plain,
( ( ~ p(b)
| ~ p(a) )
& ! [X] :
? [Y] :
( ~ q(d)
| ~ q(c)
| ~ q(Y)
| ~ q(X)
| p(X) )
& ! [Z] :
( q(Z)
& ( r(Z)
| p(Z) ) ) ),
inference(fof_nnf,[status(thm)],[thm119_neg]) ).
fof(sk_thm119_neg,plain,
( ( ~ p(b)
| ~ p(a) )
& ! [X] :
( ~ q(d)
| ~ q(c)
| ~ q(sK0(X))
| ~ q(X)
| p(X) )
& ! [Z] :
( q(Z)
& ( r(Z)
| p(Z) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Y,sK0(X))],[nnf_1]) ).
cnf(c_2,negated_conjecture,
( ~ p(b)
| ~ p(a) ),
inference(split_conjunct,[status(thm)],[sk_thm119_neg]) ).
cnf(c_3,negated_conjecture,
( ~ q(d)
| ~ q(c)
| ~ q(sK0(A))
| ~ q(A)
| p(A) ),
inference(split_conjunct,[status(thm)],[sk_thm119_neg]) ).
cnf(c_4,negated_conjecture,
q(A),
inference(split_conjunct,[status(thm)],[sk_thm119_neg]) ).
cnf(c_7,negated_conjecture,
( ~ q(d)
| ~ q(c)
| ~ q(sK0(A))
| p(A) ),
inference(resolve,[status(thm)],[c_4,c_3]) ).
cnf(c_8,negated_conjecture,
( ~ q(d)
| ~ q(c)
| p(A) ),
inference(resolve,[status(thm)],[c_4,c_7]) ).
cnf(c_9,negated_conjecture,
( ~ q(d)
| p(A) ),
inference(resolve,[status(thm)],[c_4,c_8]) ).
cnf(c_5,negated_conjecture,
p(A),
inference(resolve,[status(thm)],[c_4,c_9]) ).
cnf(c_10,negated_conjecture,
~ p(b),
inference(resolve,[status(thm)],[c_5,c_2]) ).
cnf(c_6,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_5,c_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN722+1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n003.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 18:23:54 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 3501111 was started by sandbox2 on n003,
% 0.09/0.37 % Sat Sep 26 18:23:54 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.39
% 0.09/0.39 % SZS status Theorem for theBenchmark
% 0.09/0.39
% 0.09/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.39 % Length of proof is 6.
% 0.09/0.39 % Level of proof is 3.
% 0.09/0.39 % Maximum clause weight is 11.000.
% 0.09/0.39 % Given clauses 0.
% 0.09/0.39
% 0.09/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------