%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MSC017+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 08:04:29 AM UTC 2026
% Result : Theorem 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 28 ( 10 unt; 0 def)
% Number of atoms : 63 ( 5 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 61 ( 26 ~; 18 |; 6 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-1 aty)
% Number of variables : 18 ( 0 sgn 9 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(depth_and_time_and_nitrogen,axiom,
! [D] :
( dive(D)
=> ( ( greater(time(D),time_limit)
| greater(depth(D),depth_limit) )
<=> greater(nitrogen(D),nitrogen_limit) ) ),
file('theBenchmark.p',depth_and_time_and_nitrogen) ).
fof(too_much_nitrogen,axiom,
! [D] :
( dive(D)
=> ( greater(nitrogen(D),nitrogen_limit)
<=> outcome(D,dci) ) ),
file('theBenchmark.p',too_much_nitrogen) ).
fof(dci_is_the_only_bad_outcome,axiom,
! [D] :
( dive(D)
=> ! [O] :
( ( bad(O)
& outcome(D,O) )
=> O = dci ) ),
file('theBenchmark.p',dci_is_the_only_bad_outcome) ).
fof(no_deep_long,axiom,
! [D] :
( dive(D)
=> ( ~ greater(time(D),time_limit)
& ~ greater(depth(D),depth_limit) ) ),
file('theBenchmark.p',no_deep_long) ).
fof(no_bad,conjecture,
! [D] :
( dive(D)
=> ! [O] :
( outcome(D,O)
=> ~ bad(O) ) ),
file('theBenchmark.p',no_bad) ).
fof(no_bad_neg,negated_conjecture,
~ ! [D] :
( dive(D)
=> ! [O] :
( outcome(D,O)
=> ~ bad(O) ) ),
inference(assume_negation,[status(cth)],[no_bad]) ).
fof(nnf_6,plain,
? [D] :
( ? [O] :
( bad(O)
& outcome(D,O) )
& dive(D) ),
inference(fof_nnf,[status(thm)],[no_bad_neg]) ).
fof(sk_no_bad_neg,plain,
( bad(sK1)
& outcome(sK0,sK1)
& dive(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(D,sK0),skolemize(O,sK1)],[nnf_6]) ).
cnf(c_7,negated_conjecture,
dive(sK0),
inference(split_conjunct,[status(thm)],[sk_no_bad_neg]) ).
cnf(c_8,plain,
( ~ greater(time(A),time_limit)
| ~ dive(A) ),
inference(clausify,[status(thm)],[no_deep_long]) ).
cnf(c_9,plain,
( ~ greater(depth(A),depth_limit)
| ~ dive(A) ),
inference(clausify,[status(thm)],[no_deep_long]) ).
cnf(c_10,plain,
( B = dci
| ~ bad(B)
| ~ outcome(A,B)
| ~ dive(A) ),
inference(clausify,[status(thm)],[dci_is_the_only_bad_outcome]) ).
cnf(c_11,plain,
( ~ outcome(A,dci)
| greater(nitrogen(A),nitrogen_limit)
| ~ dive(A) ),
inference(clausify,[status(thm)],[too_much_nitrogen]) ).
cnf(c_13,plain,
( ~ greater(nitrogen(A),nitrogen_limit)
| greater(time(A),time_limit)
| greater(depth(A),depth_limit)
| ~ dive(A) ),
inference(clausify,[status(thm)],[depth_and_time_and_nitrogen]) ).
cnf(c_17,negated_conjecture,
bad(sK1),
inference(split_conjunct,[status(thm)],[sk_no_bad_neg]) ).
cnf(c_18,negated_conjecture,
( A = dci
| ~ bad(A)
| ~ outcome(sK0,A) ),
inference(resolve,[status(thm)],[c_7,c_10]) ).
cnf(c_20,negated_conjecture,
( sK1 = dci
| ~ outcome(sK0,sK1) ),
inference(resolve,[status(thm)],[c_17,c_18]) ).
cnf(c_21,negated_conjecture,
outcome(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_no_bad_neg]) ).
cnf(c_22,negated_conjecture,
~ greater(time(sK0),time_limit),
inference(resolve,[status(thm)],[c_7,c_8]) ).
cnf(c_23,negated_conjecture,
~ greater(depth(sK0),depth_limit),
inference(resolve,[status(thm)],[c_7,c_9]) ).
cnf(c_24,negated_conjecture,
( ~ outcome(sK0,dci)
| greater(nitrogen(sK0),nitrogen_limit) ),
inference(resolve,[status(thm)],[c_7,c_11]) ).
cnf(c_26,negated_conjecture,
( ~ greater(nitrogen(sK0),nitrogen_limit)
| greater(time(sK0),time_limit)
| greater(depth(sK0),depth_limit) ),
inference(resolve,[status(thm)],[c_7,c_13]) ).
cnf(c_32,negated_conjecture,
( ~ greater(nitrogen(sK0),nitrogen_limit)
| greater(time(sK0),time_limit) ),
inference(resolve,[status(thm)],[c_23,c_26]) ).
cnf(c_27,negated_conjecture,
~ greater(nitrogen(sK0),nitrogen_limit),
inference(resolve,[status(thm)],[c_22,c_32]) ).
cnf(c_29,negated_conjecture,
sK1 = dci,
inference(resolve,[status(thm)],[c_21,c_20]) ).
cnf(c_30,negated_conjecture,
~ outcome(sK0,dci),
inference(resolve,[status(thm)],[c_27,c_24]) ).
cnf(c_33,negated_conjecture,
outcome(sK0,dci),
inference(paramod,[status(thm)],[c_29,c_21]) ).
cnf(c_31,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_30,c_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MSC017+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 00:17:21 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 320994 was started by sandbox2 on n004,
% 0.11/0.37 % Sat Sep 26 00:17:21 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.11/0.39
% 0.11/0.39 % SZS status Theorem for theBenchmark
% 0.11/0.39
% 0.11/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.39 % Length of proof is 23.
% 0.11/0.39 % Level of proof is 5.
% 0.11/0.39 % Maximum clause weight is 7.000.
% 0.11/0.39 % Given clauses 0.
% 0.11/0.39
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------