%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT036+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 : n006.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 0.09s 5.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 40 ( 10 unt; 0 def)
% Number of atoms : 113 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 134 ( 61 ~; 50 |; 14 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 99 ( 24 sgn 22 !; 2 ?)
% 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(mp_time_point_occur,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> in_environment(E,T) ),
file('theBenchmark.p',mp_time_point_occur) ).
fof(mp_growth_rate_relationships,axiom,
! [E,S1,S2,T] :
( ( ( subpopulations(S1,S2,E,T)
& environment(E) )
=> greater_or_equal(growth_rate(S1,T),zero) )
<=> ~ greater(zero,growth_rate(S1,T)) ),
file('theBenchmark.p',mp_growth_rate_relationships) ).
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,axiom,
! [E,S1,S2,T] :
( ( greater(resilience(S2),resilience(S1))
& ~ greater(zero,growth_rate(S1,T))
& in_environment(E,T)
& environment(E) )
=> ~ greater(zero,growth_rate(S2,T)) ),
file('theBenchmark.p',a13) ).
fof(prove_t5,conjecture,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ~ outcompetes(first_movers,efficient_producers,T) ),
file('theBenchmark.p',prove_t5) ).
fof(prove_t5_neg,negated_conjecture,
~ ! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> ~ outcompetes(first_movers,efficient_producers,T) ),
inference(assume_negation,[status(cth)],[prove_t5]) ).
cnf(c_7,plain,
( ~ greater(zero,growth_rate(B,C))
| environment(A) ),
inference(clausify,[status(thm)],[mp_growth_rate_relationships]) ).
cnf(c_8,plain,
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_time_point_occur]) ).
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_12,plain,
( ~ outcompetes(C,B,D)
| greater_or_equal(growth_rate(C,D),zero)
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(clausify,[status(thm)],[d2]) ).
cnf(c_13,plain,
( ~ outcompetes(C,B,D)
| greater(zero,growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(clausify,[status(thm)],[d2]) ).
cnf(c_14,plain,
( ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[a13]) ).
fof(nnf_6,plain,
? [E,T] :
( outcompetes(first_movers,efficient_producers,T)
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
inference(fof_nnf,[status(thm)],[prove_t5_neg]) ).
fof(sk_prove_t5_neg,plain,
( outcompetes(first_movers,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_6]) ).
cnf(c_15,negated_conjecture,
environment(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_t5_neg]) ).
cnf(c_16,plain,
( ~ greater(zero,growth_rate(E,F))
| ~ greater(zero,growth_rate(D,B))
| ~ greater(resilience(D),resilience(C))
| greater(zero,growth_rate(C,B))
| ~ in_environment(A,B) ),
inference(resolve,[status(thm)],[c_14,c_7]) ).
cnf(c_18,plain,
( in_environment(C,D)
| ~ subpopulations(first_movers,efficient_producers,C,D)
| ~ greater(zero,growth_rate(A,B)) ),
inference(resolve,[status(thm)],[c_7,c_8]) ).
cnf(c_20,plain,
( ~ greater(zero,growth_rate(A,B))
| ~ greater_or_equal(growth_rate(A,B),zero) ),
inference(clausify,[status(thm)],[mp_growth_rate_relationships]) ).
cnf(c_22,plain,
( ~ greater(zero,growth_rate(E,F))
| ~ outcompetes(B,A,D)
| greater_or_equal(growth_rate(B,D),zero)
| ~ subpopulations(A,B,C,D) ),
inference(resolve,[status(thm)],[c_12,c_7]) ).
cnf(c_25,plain,
( ~ greater(zero,growth_rate(B,D))
| ~ greater(zero,growth_rate(E,F))
| ~ outcompetes(B,A,D)
| ~ subpopulations(A,B,C,D) ),
inference(resolve,[status(thm)],[c_22,c_20]) ).
cnf(c_28,negated_conjecture,
( subpopulations(B,A,sK0,C)
| ~ subpopulations(A,B,sK0,C) ),
inference(resolve,[status(thm)],[c_15,c_9]) ).
cnf(c_29,negated_conjecture,
( ~ outcompetes(B,A,C)
| greater(zero,growth_rate(A,C))
| ~ subpopulations(A,B,sK0,C) ),
inference(resolve,[status(thm)],[c_15,c_13]) ).
cnf(c_32,negated_conjecture,
outcompetes(first_movers,efficient_producers,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_t5_neg]) ).
cnf(c_33,negated_conjecture,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_t5_neg]) ).
fof(a2,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('theBenchmark.p',a2) ).
cnf(c_34,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(clausify,[status(thm)],[a2]) ).
cnf(c_37,plain,
( ~ greater(zero,growth_rate(V6,V7))
| ~ greater(zero,growth_rate(F,D))
| ~ greater(resilience(F),resilience(E))
| greater(zero,growth_rate(E,D))
| ~ subpopulations(first_movers,efficient_producers,C,D)
| ~ greater(zero,growth_rate(A,B)) ),
inference(resolve,[status(thm)],[c_18,c_16]) ).
cnf(c_38,plain,
( ~ greater(zero,growth_rate(B,D))
| ~ outcompetes(B,A,D)
| ~ subpopulations(A,B,C,D) ),
inference(factor,[status(thm)],[c_25]) ).
cnf(c_42,plain,
( ~ greater(zero,growth_rate(E,F))
| ~ greater(resilience(A),resilience(D))
| greater(zero,growth_rate(D,B))
| ~ subpopulations(first_movers,efficient_producers,C,B)
| ~ greater(zero,growth_rate(A,B)) ),
inference(factor,[status(thm)],[c_37]) ).
cnf(c_45,plain,
( ~ greater(resilience(A),resilience(D))
| greater(zero,growth_rate(D,B))
| ~ subpopulations(first_movers,efficient_producers,C,B)
| ~ greater(zero,growth_rate(A,B)) ),
inference(factor,[status(thm)],[c_42]) ).
cnf(c_49,plain,
subpopulations(efficient_producers,first_movers,sK0,sK1),
inference(resolve,[status(thm)],[c_33,c_28]) ).
cnf(c_55,plain,
( ~ greater(resilience(A),resilience(B))
| greater(zero,growth_rate(B,sK1))
| ~ greater(zero,growth_rate(A,sK1)) ),
inference(resolve,[status(thm)],[c_45,c_33]) ).
cnf(c_75,plain,
( ~ greater(zero,growth_rate(first_movers,sK1))
| ~ outcompetes(first_movers,efficient_producers,sK1) ),
inference(resolve,[status(thm)],[c_49,c_38]) ).
cnf(c_58,negated_conjecture,
~ greater(zero,growth_rate(first_movers,sK1)),
inference(resolve,[status(thm)],[c_32,c_75]) ).
cnf(c_76,negated_conjecture,
( ~ outcompetes(first_movers,efficient_producers,sK1)
| greater(zero,growth_rate(efficient_producers,sK1)) ),
inference(resolve,[status(thm)],[c_49,c_29]) ).
cnf(c_60,negated_conjecture,
greater(zero,growth_rate(efficient_producers,sK1)),
inference(resolve,[status(thm)],[c_32,c_76]) ).
cnf(c_77,plain,
( greater(zero,growth_rate(first_movers,sK1))
| ~ greater(zero,growth_rate(efficient_producers,sK1)) ),
inference(resolve,[status(thm)],[c_55,c_34]) ).
cnf(c_78,plain,
greater(zero,growth_rate(first_movers,sK1)),
inference(resolve,[status(thm)],[c_60,c_77]) ).
cnf(c_74,plain,
$false,
inference(resolve,[status(thm)],[c_58,c_78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT036+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.37 % Computer : n006.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Sat Sep 26 00:06:33 UTC 2026
% 0.09/5.38 % CPUTime :
% 0.09/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.38 % Process 4079669 was started by sandbox2 on n006,
% 0.09/5.38 % Sat Sep 26 00:06:33 2026
% 0.09/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.38
% 0.09/5.38 % From the command line: assign(max_seconds, 300).
% 0.09/5.40
% 0.09/5.40 % SZS status Theorem for theBenchmark
% 0.09/5.40
% 0.09/5.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/5.40 % Length of proof is 32.
% 0.09/5.40 % Level of proof is 7.
% 0.09/5.40 % Maximum clause weight is 30.000.
% 0.09/5.40 % Given clauses 19.
% 0.09/5.40
% 0.09/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------