%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT041+2 : 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 : 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 08:02:56 AM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 26 ( 8 unt; 0 def)
% Number of atoms : 64 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 64 ( 26 ~; 18 |; 18 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 22 ( 1 sgn 6 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_not_high_and_low,axiom,
! [X,T] :
~ ( number_of_routines(X,T,high)
& number_of_routines(X,T,low) ),
file('theBenchmark.p',mp_not_high_and_low) ).
fof(a14,axiom,
! [X,T] :
( ( founding_time(X,T)
& efficient_producer(X)
& organisation_at_time(X,T) )
=> has_elaborated_routines(X,T) ),
file('theBenchmark.p',a14) ).
fof(a15,axiom,
! [X,T] :
( ( founding_time(X,T)
& first_mover(X)
& organisation_at_time(X,T) )
=> number_of_routines(X,T,low) ),
file('theBenchmark.p',a15) ).
fof(a16,axiom,
? [X,T] :
( ~ has_elaborated_routines(X,T)
& number_of_routines(X,T,high)
& founding_time(X,T)
& organisation_at_time(X,T) ),
file('theBenchmark.p',a16) ).
fof(prove_t10,conjecture,
? [X,T] :
( ~ efficient_producer(X)
& ~ first_mover(X)
& organisation_at_time(X,T) ),
file('theBenchmark.p',prove_t10) ).
fof(prove_t10_neg,negated_conjecture,
~ ? [X,T] :
( ~ efficient_producer(X)
& ~ first_mover(X)
& organisation_at_time(X,T) ),
inference(assume_negation,[status(cth)],[prove_t10]) ).
fof(nnf_4,plain,
? [X,T] :
( ~ has_elaborated_routines(X,T)
& number_of_routines(X,T,high)
& founding_time(X,T)
& organisation_at_time(X,T) ),
inference(fof_nnf,[status(thm)],[a16]) ).
fof(sk_a16,plain,
( ~ has_elaborated_routines(sK0,sK1)
& number_of_routines(sK0,sK1,high)
& founding_time(sK0,sK1)
& organisation_at_time(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X,sK0),skolemize(T,sK1)],[nnf_4]) ).
cnf(c_6,plain,
organisation_at_time(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_a16]) ).
cnf(c_7,plain,
( number_of_routines(A,B,low)
| ~ founding_time(A,B)
| ~ first_mover(A)
| ~ organisation_at_time(A,B) ),
inference(clausify,[status(thm)],[a15]) ).
cnf(c_8,plain,
( has_elaborated_routines(A,B)
| ~ founding_time(A,B)
| ~ efficient_producer(A)
| ~ organisation_at_time(A,B) ),
inference(clausify,[status(thm)],[a14]) ).
cnf(c_9,negated_conjecture,
( efficient_producer(A)
| first_mover(A)
| ~ organisation_at_time(A,B) ),
inference(clausify,[status(thm)],[prove_t10_neg]) ).
cnf(c_10,plain,
( has_elaborated_routines(sK0,sK1)
| ~ founding_time(sK0,sK1)
| ~ efficient_producer(sK0) ),
inference(resolve,[status(thm)],[c_6,c_8]) ).
cnf(c_11,negated_conjecture,
( efficient_producer(sK0)
| first_mover(sK0) ),
inference(resolve,[status(thm)],[c_9,c_6]) ).
cnf(c_12,plain,
founding_time(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_a16]) ).
cnf(c_13,negated_conjecture,
( first_mover(sK0)
| has_elaborated_routines(sK0,sK1)
| ~ founding_time(sK0,sK1) ),
inference(resolve,[status(thm)],[c_10,c_11]) ).
cnf(c_14,plain,
( number_of_routines(sK0,sK1,low)
| ~ founding_time(sK0,sK1)
| ~ first_mover(sK0) ),
inference(resolve,[status(thm)],[c_6,c_7]) ).
cnf(c_15,plain,
~ has_elaborated_routines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_a16]) ).
cnf(c_16,negated_conjecture,
( first_mover(sK0)
| has_elaborated_routines(sK0,sK1) ),
inference(resolve,[status(thm)],[c_12,c_13]) ).
cnf(c_17,plain,
( number_of_routines(sK0,sK1,low)
| ~ first_mover(sK0) ),
inference(resolve,[status(thm)],[c_14,c_12]) ).
cnf(c_18,negated_conjecture,
first_mover(sK0),
inference(resolve,[status(thm)],[c_15,c_16]) ).
cnf(c_19,negated_conjecture,
number_of_routines(sK0,sK1,low),
inference(resolve,[status(thm)],[c_17,c_18]) ).
cnf(c_20,plain,
number_of_routines(sK0,sK1,high),
inference(split_conjunct,[status(thm)],[sk_a16]) ).
cnf(c_21,plain,
( ~ number_of_routines(A,B,high)
| ~ number_of_routines(A,B,low) ),
inference(clausify,[status(thm)],[mp_not_high_and_low]) ).
cnf(c_23,negated_conjecture,
~ number_of_routines(sK0,sK1,high),
inference(resolve,[status(thm)],[c_21,c_19]) ).
cnf(c_22,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_20,c_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT041+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 00:10:08 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1475638 was started by sandbox on n003,
% 0.09/0.36 % Sat Sep 26 00:10:08 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 22.
% 0.13/0.38 % Level of proof is 7.
% 0.13/0.38 % Maximum clause weight is 8.000.
% 0.13/0.38 % Given clauses 3.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------