%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT036+3 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 08:02:54 AM UTC 2026
% Result : Theorem 0.13s 0.37s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 23 ( 7 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 58 ( 22 ~; 17 |; 16 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 8 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_symmetry_of_subpopulations,axiom,
! [E,S1,S2,T] :
( ( subpopulations(S1,S2,E,T)
& environment(E) )
=> subpopulations(S2,S1,E,T) ),
file('theBenchmark.p',mp_symmetry_of_subpopulations) ).
fof(d2,axiom,
! [E,S1,S2,T] :
( ( subpopulations(S1,S2,E,T)
& environment(E) )
=> ( ( greater(zero,growth_rate(S1,T))
& greater_or_equal(growth_rate(S2,T),zero) )
<=> outcompetes(S2,S1,T) ) ),
file('theBenchmark.p',d2) ).
fof(a13_star,axiom,
? [E,T] :
( greater(zero,growth_rate(efficient_producers,T))
& greater_or_equal(growth_rate(first_movers,T),zero)
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
file('theBenchmark.p',a13_star) ).
fof(prove_t5_star,conjecture,
? [E,T] :
( outcompetes(first_movers,efficient_producers,T)
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
file('theBenchmark.p',prove_t5_star) ).
fof(prove_t5_star_neg,negated_conjecture,
~ ? [E,T] :
( outcompetes(first_movers,efficient_producers,T)
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
inference(assume_negation,[status(cth)],[prove_t5_star]) ).
fof(nnf_3,plain,
? [E,T] :
( greater(zero,growth_rate(efficient_producers,T))
& greater_or_equal(growth_rate(first_movers,T),zero)
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
inference(fof_nnf,[status(thm)],[a13_star]) ).
fof(sk_a13_star,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
& greater_or_equal(growth_rate(first_movers,sK1),zero)
& subpopulations(first_movers,efficient_producers,sK0,sK1)
& environment(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(E,sK0),skolemize(T,sK1)],[nnf_3]) ).
cnf(c_5,plain,
environment(sK0),
inference(split_conjunct,[status(thm)],[sk_a13_star]) ).
cnf(c_8,plain,
( outcompetes(C,B,D)
| ~ greater(zero,growth_rate(B,D))
| ~ greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(clausify,[status(thm)],[d2]) ).
cnf(c_9,plain,
( subpopulations(C,B,A,D)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_symmetry_of_subpopulations]) ).
cnf(c_10,negated_conjecture,
( ~ outcompetes(first_movers,efficient_producers,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[prove_t5_star_neg]) ).
cnf(c_12,plain,
( outcompetes(B,A,C)
| ~ greater(zero,growth_rate(A,C))
| ~ greater_or_equal(growth_rate(B,C),zero)
| ~ subpopulations(A,B,sK0,C) ),
inference(resolve,[status(thm)],[c_5,c_8]) ).
cnf(c_13,plain,
greater_or_equal(growth_rate(first_movers,sK1),zero),
inference(split_conjunct,[status(thm)],[sk_a13_star]) ).
cnf(c_14,plain,
greater(zero,growth_rate(efficient_producers,sK1)),
inference(split_conjunct,[status(thm)],[sk_a13_star]) ).
cnf(c_16,plain,
( outcompetes(first_movers,A,sK1)
| ~ greater(zero,growth_rate(A,sK1))
| ~ subpopulations(A,first_movers,sK0,sK1) ),
inference(resolve,[status(thm)],[c_13,c_12]) ).
cnf(c_20,plain,
( outcompetes(first_movers,efficient_producers,sK1)
| ~ subpopulations(efficient_producers,first_movers,sK0,sK1) ),
inference(resolve,[status(thm)],[c_14,c_16]) ).
cnf(c_22,negated_conjecture,
( ~ outcompetes(first_movers,efficient_producers,A)
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_10,c_5]) ).
cnf(c_23,plain,
( subpopulations(B,A,sK0,C)
| ~ subpopulations(A,B,sK0,C) ),
inference(resolve,[status(thm)],[c_5,c_9]) ).
cnf(c_24,plain,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_a13_star]) ).
cnf(c_31,negated_conjecture,
( ~ subpopulations(efficient_producers,first_movers,sK0,sK1)
| ~ subpopulations(first_movers,efficient_producers,sK0,sK1) ),
inference(resolve,[status(thm)],[c_22,c_20]) ).
cnf(c_26,negated_conjecture,
~ subpopulations(efficient_producers,first_movers,sK0,sK1),
inference(resolve,[status(thm)],[c_24,c_31]) ).
cnf(c_32,plain,
subpopulations(efficient_producers,first_movers,sK0,sK1),
inference(resolve,[status(thm)],[c_23,c_24]) ).
cnf(c_30,plain,
$false,
inference(resolve,[status(thm)],[c_26,c_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT036+3 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.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
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 00:06:29 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 2890598 was started by sandbox2 on n009,
% 0.09/0.35 % Sat Sep 26 00:06:29 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.37
% 0.13/0.37 % SZS status Theorem for theBenchmark
% 0.13/0.37
% 0.13/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.37 % Length of proof is 18.
% 0.13/0.37 % Level of proof is 6.
% 0.13/0.37 % Maximum clause weight is 10.000.
% 0.13/0.37 % Given clauses 7.
% 0.13/0.37
% 0.13/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------