%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT032+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 : n016.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 08:02:32 AM UTC 2026
% Result : Theorem 0.32s 15.42s
% Output : CNFRefutation 0.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 5 unt; 0 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 162 ( 70 ~; 59 |; 26 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 47 ( 0 sgn 22 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp1_high_growth_rates,axiom,
! [E,S1,S2,T] :
( ( greater(growth_rate(S2,T),growth_rate(S1,T))
& subpopulations(S1,S2,E,T)
& environment(E) )
=> selection_favors(S2,S1,T) ),
file('theBenchmark.p',mp1_high_growth_rates) ).
fof(l1,axiom,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T)) )
& in_environment(E,To) ) ),
file('theBenchmark.p',l1) ).
fof(prove_t1,conjecture,
! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> selection_favors(efficient_producers,first_movers,T) )
& in_environment(E,To) ) ),
file('theBenchmark.p',prove_t1) ).
fof(prove_t1_neg,negated_conjecture,
~ ! [E] :
( ( stable(E)
& environment(E) )
=> ? [To] :
( ! [T] :
( ( greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
=> selection_favors(efficient_producers,first_movers,T) )
& in_environment(E,To) ) ),
inference(assume_negation,[status(cth)],[prove_t1]) ).
fof(nnf_3,plain,
? [E] :
( ! [To] :
( ? [T] :
( ~ selection_favors(efficient_producers,first_movers,T)
& greater_or_equal(T,To)
& subpopulations(first_movers,efficient_producers,E,T) )
| ~ in_environment(E,To) )
& stable(E)
& environment(E) ),
inference(fof_nnf,[status(thm)],[prove_t1_neg]) ).
fof(sk_prove_t1_neg_sk,plain,
( ! [To] :
( ( ~ selection_favors(efficient_producers,first_movers,sK2(To))
& greater_or_equal(sK2(To),To)
& subpopulations(first_movers,efficient_producers,sK0,sK2(To)) )
| ~ in_environment(sK0,To) )
& stable(sK0)
& environment(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2]),skolemize(E,sK0),skolemize(T,sK2(To))],[nnf_3]) ).
fof(sk_prove_t1_neg,plain,
( ! [VAR_0] :
( ~ selection_favors(efficient_producers,first_movers,sK2(VAR_0))
| ~ in_environment(sK0,VAR_0) )
& ! [VAR_0] :
( greater_or_equal(sK2(VAR_0),VAR_0)
| ~ in_environment(sK0,VAR_0) )
& ! [VAR_0] :
( subpopulations(first_movers,efficient_producers,sK0,sK2(VAR_0))
| ~ in_environment(sK0,VAR_0) )
& stable(sK0)
& environment(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_prove_t1_neg_sk]) ).
cnf(c_4,negated_conjecture,
environment(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_t1_neg]) ).
fof(nnf_2,plain,
! [E] :
( ? [To] :
( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater_or_equal(T,To)
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& in_environment(E,To) )
| ~ stable(E)
| ~ environment(E) ),
inference(fof_nnf,[status(thm)],[l1]) ).
fof(sk_l1_sk,plain,
! [E] :
( ( ! [T] :
( greater(growth_rate(efficient_producers,T),growth_rate(first_movers,T))
| ~ greater_or_equal(T,sK1(E))
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& in_environment(E,sK1(E)) )
| ~ stable(E)
| ~ environment(E) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(To,sK1(E))],[nnf_2]) ).
fof(sk_l1,plain,
( ! [VAR_0,VAR_1] :
( greater(growth_rate(efficient_producers,VAR_1),growth_rate(first_movers,VAR_1))
| ~ greater_or_equal(VAR_1,sK1(VAR_0))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ stable(VAR_0)
| ~ environment(VAR_0) )
& ! [VAR_0] :
( in_environment(VAR_0,sK1(VAR_0))
| ~ stable(VAR_0)
| ~ environment(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_l1_sk]) ).
cnf(c_5,plain,
( greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ greater_or_equal(B,sK1(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_l1]) ).
cnf(c_6,plain,
( in_environment(A,sK1(A))
| ~ stable(A)
| ~ environment(A) ),
inference(split_conjunct,[status(thm)],[sk_l1]) ).
cnf(c_7,plain,
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp1_high_growth_rates]) ).
cnf(c_8,negated_conjecture,
( subpopulations(first_movers,efficient_producers,sK0,sK2(A))
| ~ in_environment(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_prove_t1_neg]) ).
cnf(c_9,negated_conjecture,
( greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ greater_or_equal(A,sK1(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,A)
| ~ stable(sK0) ),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_10,negated_conjecture,
( selection_favors(B,A,C)
| ~ greater(growth_rate(B,C),growth_rate(A,C))
| ~ subpopulations(A,B,sK0,C) ),
inference(resolve,[status(thm)],[c_4,c_7]) ).
cnf(c_11,negated_conjecture,
( greater(growth_rate(efficient_producers,sK2(A)),growth_rate(first_movers,sK2(A)))
| ~ greater_or_equal(sK2(A),sK1(sK0))
| ~ stable(sK0)
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_8,c_9]) ).
cnf(c_12,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK2(A))
| ~ greater(growth_rate(efficient_producers,sK2(A)),growth_rate(first_movers,sK2(A)))
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_8,c_10]) ).
cnf(c_13,negated_conjecture,
( ~ selection_favors(efficient_producers,first_movers,sK2(A))
| ~ in_environment(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_prove_t1_neg]) ).
cnf(c_14,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK2(A))
| ~ in_environment(sK0,A)
| ~ greater_or_equal(sK2(A),sK1(sK0))
| ~ stable(sK0)
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_11,c_12]) ).
cnf(c_15,negated_conjecture,
stable(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_t1_neg]) ).
cnf(c_16,negated_conjecture,
( ~ in_environment(sK0,A)
| ~ greater_or_equal(sK2(A),sK1(sK0))
| ~ stable(sK0)
| ~ in_environment(sK0,A)
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_13,c_14]) ).
cnf(c_17,negated_conjecture,
( in_environment(sK0,sK1(sK0))
| ~ stable(sK0) ),
inference(resolve,[status(thm)],[c_4,c_6]) ).
cnf(c_18,negated_conjecture,
( greater_or_equal(sK2(A),A)
| ~ in_environment(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_prove_t1_neg]) ).
cnf(c_19,negated_conjecture,
( ~ in_environment(sK0,A)
| ~ greater_or_equal(sK2(A),sK1(sK0))
| ~ in_environment(sK0,A)
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_15,c_16]) ).
cnf(c_20,negated_conjecture,
( ~ in_environment(sK0,sK1(sK0))
| ~ in_environment(sK0,sK1(sK0))
| ~ in_environment(sK0,sK1(sK0))
| ~ in_environment(sK0,sK1(sK0)) ),
inference(resolve,[status(thm)],[c_18,c_19]) ).
cnf(c_24,negated_conjecture,
( ~ in_environment(sK0,sK1(sK0))
| ~ in_environment(sK0,sK1(sK0))
| ~ in_environment(sK0,sK1(sK0)) ),
inference(copy,[status(thm)],[c_20]) ).
cnf(c_25,negated_conjecture,
( ~ in_environment(sK0,sK1(sK0))
| ~ in_environment(sK0,sK1(sK0)) ),
inference(copy,[status(thm)],[c_24]) ).
cnf(c_21,negated_conjecture,
~ in_environment(sK0,sK1(sK0)),
inference(copy,[status(thm)],[c_25]) ).
cnf(c_22,negated_conjecture,
in_environment(sK0,sK1(sK0)),
inference(resolve,[status(thm)],[c_17,c_15]) ).
cnf(c_23,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_21,c_22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT032+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n016.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.32/15.40 % CPULimit : 300
% 0.32/15.40 % WCLimit : 300
% 0.32/15.40 % DateTime : Sat Sep 26 00:08:10 UTC 2026
% 0.32/15.40 % CPUTime :
% 0.32/15.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.32/15.40 % Process 3791498 was started by sandbox on n026,
% 0.32/15.40 % Sat Sep 26 00:08:10 2026
% 0.32/15.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.32/15.41
% 0.32/15.41 % From the command line: assign(max_seconds, 300).
% 0.32/15.42
% 0.32/15.42 % SZS status Theorem for theBenchmark
% 0.32/15.42
% 0.32/15.42 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.32/15.42 % Length of proof is 23.
% 0.32/15.42 % Level of proof is 9.
% 0.32/15.42 % Maximum clause weight is 4.000.
% 0.32/15.42 % Given clauses 0.
% 0.32/15.42
% 0.32/15.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------