%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT022+2 : 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 08:02:08 AM UTC 2026
% Result : Theorem 0.16s 0.45s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 8 unt; 0 def)
% Number of atoms : 95 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 98 ( 34 ~; 34 |; 20 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 26 ( 0 sgn 9 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_constant_not_decrease,axiom,
! [X] :
( constant(X)
=> ~ decreases(X) ),
file('theBenchmark.p',mp_constant_not_decrease) ).
fof(a6,axiom,
! [E,S1,S2,T] :
( ( greater(resilience(S2),resilience(S1))
& subpopulations(S1,S2,E,T)
& environment(E) )
=> ( ( constant(resources(E,T))
=> constant(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) )
& ( decreases(resources(E,T))
=> increases(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) ) ) ),
file('theBenchmark.p',a6) ).
fof(prove_l4,conjecture,
! [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',prove_l4) ).
fof(prove_l4_neg,negated_conjecture,
~ ! [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))) ) ) ),
inference(assume_negation,[status(cth)],[prove_l4]) ).
fof(nnf_3,plain,
? [E,T] :
( ( ( decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
& constant(resources(E,T)) )
| ( ~ increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
& decreases(resources(E,T)) ) )
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
inference(fof_nnf,[status(thm)],[prove_l4_neg]) ).
fof(sk_prove_l4_neg_sk,plain,
( ( ( decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
& constant(resources(sK0,sK1)) )
| ( ~ increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
& decreases(resources(sK0,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_3]) ).
fof(sk_prove_l4_neg,plain,
( ( decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| ~ increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) )
& ( constant(resources(sK0,sK1))
| ~ increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) )
& ( decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| decreases(resources(sK0,sK1)) )
& ( constant(resources(sK0,sK1))
| decreases(resources(sK0,sK1)) )
& subpopulations(first_movers,efficient_producers,sK0,sK1)
& environment(sK0) ),
inference(cnf_transformation,[status(thm)],[sk_prove_l4_neg_sk]) ).
cnf(c_4,negated_conjecture,
environment(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_l4_neg]) ).
cnf(c_5,plain,
( constant(difference(disbanding_rate(B,D),disbanding_rate(C,D)))
| ~ constant(resources(A,D))
| ~ greater(resilience(C),resilience(B))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a6]) ).
cnf(c_6,plain,
( increases(difference(disbanding_rate(B,D),disbanding_rate(C,D)))
| ~ decreases(resources(A,D))
| ~ greater(resilience(C),resilience(B))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a6]) ).
cnf(c_7,negated_conjecture,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_l4_neg]) ).
cnf(c_8,negated_conjecture,
( constant(difference(disbanding_rate(A,C),disbanding_rate(B,C)))
| ~ constant(resources(sK0,C))
| ~ greater(resilience(B),resilience(A))
| ~ subpopulations(A,B,sK0,C) ),
inference(resolve,[status(thm)],[c_4,c_5]) ).
cnf(c_9,negated_conjecture,
( increases(difference(disbanding_rate(A,C),disbanding_rate(B,C)))
| ~ decreases(resources(sK0,C))
| ~ greater(resilience(B),resilience(A))
| ~ subpopulations(A,B,sK0,C) ),
inference(resolve,[status(thm)],[c_4,c_6]) ).
fof(a2,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('theBenchmark.p',a2) ).
cnf(c_10,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(clausify,[status(thm)],[a2]) ).
cnf(c_11,negated_conjecture,
( constant(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| ~ constant(resources(sK0,sK1))
| ~ greater(resilience(efficient_producers),resilience(first_movers)) ),
inference(resolve,[status(thm)],[c_7,c_8]) ).
cnf(c_12,negated_conjecture,
( increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| ~ decreases(resources(sK0,sK1))
| ~ greater(resilience(efficient_producers),resilience(first_movers)) ),
inference(resolve,[status(thm)],[c_7,c_9]) ).
cnf(c_14,negated_conjecture,
( increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| ~ decreases(resources(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_10,c_12]) ).
cnf(c_15,negated_conjecture,
( constant(resources(sK0,sK1))
| ~ increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) ),
inference(split_conjunct,[status(thm)],[sk_prove_l4_neg]) ).
cnf(c_16,negated_conjecture,
( ~ decreases(resources(sK0,sK1))
| constant(resources(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_15,c_14]) ).
cnf(c_18,plain,
( ~ decreases(A)
| ~ constant(A) ),
inference(clausify,[status(thm)],[mp_constant_not_decrease]) ).
cnf(c_19,negated_conjecture,
( constant(resources(sK0,sK1))
| decreases(resources(sK0,sK1)) ),
inference(split_conjunct,[status(thm)],[sk_prove_l4_neg]) ).
cnf(c_20,negated_conjecture,
( decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| decreases(resources(sK0,sK1)) ),
inference(split_conjunct,[status(thm)],[sk_prove_l4_neg]) ).
cnf(c_21,negated_conjecture,
( constant(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| ~ constant(resources(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_10,c_11]) ).
cnf(c_22,plain,
( decreases(resources(sK0,sK1))
| constant(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) ),
inference(resolve,[status(thm)],[c_21,c_19]) ).
cnf(c_23,plain,
( ~ decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| decreases(resources(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_22,c_18]) ).
cnf(c_29,negated_conjecture,
( decreases(resources(sK0,sK1))
| decreases(resources(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_23,c_20]) ).
cnf(c_24,negated_conjecture,
decreases(resources(sK0,sK1)),
inference(copy,[status(thm)],[c_29]) ).
cnf(c_26,negated_conjecture,
constant(resources(sK0,sK1)),
inference(resolve,[status(thm)],[c_24,c_16]) ).
cnf(c_30,plain,
~ constant(resources(sK0,sK1)),
inference(resolve,[status(thm)],[c_18,c_24]) ).
cnf(c_28,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_26,c_30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : MGT022+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.43 % Computer : n009.cluster.edu
% 0.16/0.43 % Model : x86_64 x86_64
% 0.16/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.43 % Memory : 8046.5625MB
% 0.16/0.43 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Sat Sep 26 00:04:14 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/0.43 % Process 2887526 was started by sandbox2 on n009,
% 0.16/0.43 % Sat Sep 26 00:04:14 2026
% 0.16/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.16/0.44
% 0.16/0.44 % From the command line: assign(max_seconds, 300).
% 0.16/0.45
% 0.16/0.45 % SZS status Theorem for theBenchmark
% 0.16/0.45
% 0.16/0.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/0.45 % Length of proof is 24.
% 0.16/0.45 % Level of proof is 9.
% 0.16/0.45 % Maximum clause weight is 12.000.
% 0.16/0.45 % Given clauses 9.
% 0.16/0.45
% 0.16/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------