%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT021+1 : 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 : n020.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 08:02:08 AM UTC 2026
% Result : Theorem 0.10s 0.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 10 unt; 0 def)
% Number of atoms : 104 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 116 ( 51 ~; 41 |; 13 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 13 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_time_point_in_environment,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> in_environment(E,T) ),
file('theBenchmark.p',mp_time_point_in_environment) ).
fof(mp_environment_not_empty,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> greater(number_of_organizations(E,T),zero) ),
file('theBenchmark.p',mp_environment_not_empty) ).
fof(mp_increase_not_decrease,axiom,
! [X] :
( increases(X)
=> ~ decreases(X) ),
file('theBenchmark.p',mp_increase_not_decrease) ).
fof(a3,axiom,
! [E,T] :
( ( greater(number_of_organizations(E,T),zero)
& in_environment(E,T)
& environment(E) )
=> ( ( ~ greater(equilibrium(E),T)
=> constant(resources(E,T)) )
& ( greater(equilibrium(E),T)
=> decreases(resources(E,T)) ) ) ),
file('theBenchmark.p',a3) ).
fof(l4,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ( ( constant(resources(E,T))
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) )
& ( decreases(resources(E,T))
=> increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) ) ),
file('theBenchmark.p',l4) ).
fof(prove_l3,conjecture,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ),
file('theBenchmark.p',prove_l3) ).
fof(prove_l3_neg,negated_conjecture,
~ ! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ),
inference(assume_negation,[status(cth)],[prove_l3]) ).
fof(nnf_7,plain,
? [E,T] :
( decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
inference(fof_nnf,[status(thm)],[prove_l3_neg]) ).
fof(sk_prove_l3_neg,plain,
( decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
& 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_7]) ).
cnf(c_8,negated_conjecture,
environment(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_l3_neg]) ).
cnf(c_9,plain,
( ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ constant(resources(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l4]) ).
cnf(c_10,plain,
( increases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ decreases(resources(A,B))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l4]) ).
cnf(c_11,plain,
( constant(resources(A,B))
| greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a3]) ).
cnf(c_12,plain,
( decreases(resources(A,B))
| ~ greater(equilibrium(A),B)
| ~ greater(number_of_organizations(A,B),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a3]) ).
cnf(c_13,plain,
( greater(number_of_organizations(A,B),zero)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_environment_not_empty]) ).
cnf(c_14,plain,
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_time_point_in_environment]) ).
cnf(c_15,plain,
( ~ decreases(A)
| ~ increases(A) ),
inference(clausify,[status(thm)],[mp_increase_not_decrease]) ).
cnf(c_16,negated_conjecture,
( increases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A)))
| ~ decreases(resources(sK0,A))
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_8,c_10]) ).
cnf(c_17,negated_conjecture,
( in_environment(sK0,A)
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_8,c_14]) ).
cnf(c_18,negated_conjecture,
( greater(number_of_organizations(sK0,A),zero)
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_8,c_13]) ).
cnf(c_19,negated_conjecture,
( decreases(resources(sK0,A))
| ~ greater(equilibrium(sK0),A)
| ~ greater(number_of_organizations(sK0,A),zero)
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_8,c_12]) ).
cnf(c_20,negated_conjecture,
( constant(resources(sK0,A))
| greater(equilibrium(sK0),A)
| ~ greater(number_of_organizations(sK0,A),zero)
| ~ in_environment(sK0,A) ),
inference(resolve,[status(thm)],[c_8,c_11]) ).
cnf(c_21,negated_conjecture,
( ~ decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A)))
| ~ constant(resources(sK0,A))
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_8,c_9]) ).
cnf(c_22,negated_conjecture,
decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))),
inference(split_conjunct,[status(thm)],[sk_prove_l3_neg]) ).
cnf(c_23,negated_conjecture,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_l3_neg]) ).
cnf(c_24,negated_conjecture,
( ~ decreases(resources(sK0,A))
| ~ subpopulations(first_movers,efficient_producers,sK0,A)
| ~ decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A))) ),
inference(resolve,[status(thm)],[c_15,c_16]) ).
cnf(c_31,negated_conjecture,
( ~ decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| ~ constant(resources(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_23,c_21]) ).
cnf(c_25,negated_conjecture,
~ constant(resources(sK0,sK1)),
inference(resolve,[status(thm)],[c_22,c_31]) ).
cnf(c_26,plain,
greater(number_of_organizations(sK0,sK1),zero),
inference(resolve,[status(thm)],[c_23,c_18]) ).
cnf(c_27,plain,
in_environment(sK0,sK1),
inference(resolve,[status(thm)],[c_23,c_17]) ).
cnf(c_32,negated_conjecture,
( ~ decreases(resources(sK0,sK1))
| ~ decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) ),
inference(resolve,[status(thm)],[c_24,c_23]) ).
cnf(c_28,negated_conjecture,
~ decreases(resources(sK0,sK1)),
inference(resolve,[status(thm)],[c_22,c_32]) ).
cnf(c_33,negated_conjecture,
( constant(resources(sK0,sK1))
| greater(equilibrium(sK0),sK1)
| ~ greater(number_of_organizations(sK0,sK1),zero) ),
inference(resolve,[status(thm)],[c_27,c_20]) ).
cnf(c_34,negated_conjecture,
( constant(resources(sK0,sK1))
| greater(equilibrium(sK0),sK1) ),
inference(resolve,[status(thm)],[c_26,c_33]) ).
cnf(c_29,negated_conjecture,
greater(equilibrium(sK0),sK1),
inference(resolve,[status(thm)],[c_25,c_34]) ).
cnf(c_35,negated_conjecture,
( decreases(resources(sK0,sK1))
| ~ greater(equilibrium(sK0),sK1)
| ~ greater(number_of_organizations(sK0,sK1),zero) ),
inference(resolve,[status(thm)],[c_27,c_19]) ).
cnf(c_36,negated_conjecture,
( decreases(resources(sK0,sK1))
| ~ greater(equilibrium(sK0),sK1) ),
inference(resolve,[status(thm)],[c_26,c_35]) ).
cnf(c_37,negated_conjecture,
decreases(resources(sK0,sK1)),
inference(resolve,[status(thm)],[c_29,c_36]) ).
cnf(c_30,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_28,c_37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT021+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 00:05:05 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 4148864 was started by sandbox2 on n020,
% 0.10/0.37 % Sat Sep 26 00:05:05 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.39
% 0.10/0.39 % SZS status Theorem for theBenchmark
% 0.10/0.39
% 0.10/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/0.39 % Length of proof is 29.
% 0.10/0.39 % Level of proof is 5.
% 0.10/0.39 % Maximum clause weight is 17.000.
% 0.10/0.39 % Given clauses 11.
% 0.10/0.39
% 0.10/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------