%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT020+1 : 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 : n004.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 0.09s 0.59s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 56 ( 12 unt; 0 def)
% Number of atoms : 152 ( 13 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 157 ( 61 ~; 67 |; 16 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 0 sgn 21 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l3,axiom,
! [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',l3) ).
fof(mp_earliest_time_point,axiom,
! [E,T] :
( environment(E)
=> ( ( subpopulations(first_movers,efficient_producers,E,T)
=> greater_or_equal(T,initial_FM_EP(E)) )
& ( in_environment(E,initial_FM_EP(E))
=> subpopulations(first_movers,efficient_producers,E,initial_FM_EP(E)) ) ) ),
file('theBenchmark.p',mp_earliest_time_point) ).
fof(mp_positive_function_difference,axiom,
! [E,T,T1,T2] :
( ( greater(disbanding_rate(first_movers,T1),disbanding_rate(efficient_producers,T1))
& subpopulations(first_movers,efficient_producers,E,T2)
& greater_or_equal(T2,T)
& greater_or_equal(T,T1)
& environment(E) )
=> ( ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
=> greater(disbanding_rate(first_movers,T2),disbanding_rate(efficient_producers,T2)) ) ),
file('theBenchmark.p',mp_positive_function_difference) ).
fof(mp_time_point_occurs,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> in_environment(E,T) ),
file('theBenchmark.p',mp_time_point_occurs) ).
fof(mp_initial_time,axiom,
! [E] :
( environment(E)
=> greater_or_equal(initial_FM_EP(E),start_time(E)) ),
file('theBenchmark.p',mp_initial_time) ).
fof(mp_times_in_order,axiom,
! [E,T1,T2] :
( ( in_environment(E,T2)
& greater(T2,T1)
& greater_or_equal(T1,start_time(E))
& environment(E) )
=> in_environment(E,T1) ),
file('theBenchmark.p',mp_times_in_order) ).
fof(mp_greater_or_equal,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
=> ( X = Y
| greater(X,Y) ) ),
file('theBenchmark.p',mp_greater_or_equal) ).
fof(a8,axiom,
! [E] :
( environment(E)
=> greater(disbanding_rate(first_movers,initial_FM_EP(E)),disbanding_rate(efficient_producers,initial_FM_EP(E))) ),
file('theBenchmark.p',a8) ).
fof(prove_l2,conjecture,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> greater(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)) ),
file('theBenchmark.p',prove_l2) ).
fof(prove_l2_neg,negated_conjecture,
~ ! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> greater(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)) ),
inference(assume_negation,[status(cth)],[prove_l2]) ).
fof(nnf_11,plain,
? [E,T] :
( ~ greater(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_l2_neg]) ).
fof(sk_prove_l2_neg,plain,
( ~ greater(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_11]) ).
cnf(c_12,negated_conjecture,
environment(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_l2_neg]) ).
cnf(c_14,plain,
( greater(disbanding_rate(first_movers,initial_FM_EP(A)),disbanding_rate(efficient_producers,initial_FM_EP(A)))
| ~ environment(A) ),
inference(clausify,[status(thm)],[a8]) ).
cnf(c_15,plain,
( in_environment(A,B)
| ~ in_environment(A,C)
| ~ greater(C,B)
| ~ greater_or_equal(B,start_time(A))
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_times_in_order]) ).
cnf(c_16,plain,
( greater_or_equal(initial_FM_EP(A),start_time(A))
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_initial_time]) ).
cnf(c_17,plain,
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_time_point_occurs]) ).
cnf(c_18,plain,
( greater(disbanding_rate(first_movers,D),disbanding_rate(efficient_producers,D))
| decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ greater(disbanding_rate(first_movers,C),disbanding_rate(efficient_producers,C))
| ~ subpopulations(first_movers,efficient_producers,A,D)
| ~ greater_or_equal(D,B)
| ~ greater_or_equal(B,C)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_positive_function_difference]) ).
cnf(c_19,plain,
( greater_or_equal(B,initial_FM_EP(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_earliest_time_point]) ).
cnf(c_20,plain,
( subpopulations(first_movers,efficient_producers,A,initial_FM_EP(A))
| ~ in_environment(A,initial_FM_EP(A))
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_earliest_time_point]) ).
cnf(c_21,plain,
( ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l3]) ).
cnf(c_22,negated_conjecture,
( ~ decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A)))
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_12,c_21]) ).
cnf(c_23,negated_conjecture,
( subpopulations(first_movers,efficient_producers,sK0,initial_FM_EP(sK0))
| ~ in_environment(sK0,initial_FM_EP(sK0)) ),
inference(resolve,[status(thm)],[c_12,c_20]) ).
cnf(c_24,negated_conjecture,
( greater_or_equal(A,initial_FM_EP(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_12,c_19]) ).
cnf(c_25,negated_conjecture,
( greater(disbanding_rate(first_movers,C),disbanding_rate(efficient_producers,C))
| decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A)))
| ~ greater(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))
| ~ subpopulations(first_movers,efficient_producers,sK0,C)
| ~ greater_or_equal(C,A)
| ~ greater_or_equal(A,B) ),
inference(resolve,[status(thm)],[c_12,c_18]) ).
cnf(c_26,negated_conjecture,
( in_environment(sK0,A)
| ~ subpopulations(first_movers,efficient_producers,sK0,A) ),
inference(resolve,[status(thm)],[c_12,c_17]) ).
cnf(c_27,negated_conjecture,
greater_or_equal(initial_FM_EP(sK0),start_time(sK0)),
inference(resolve,[status(thm)],[c_12,c_16]) ).
cnf(c_28,negated_conjecture,
( in_environment(sK0,A)
| ~ in_environment(sK0,B)
| ~ greater(B,A)
| ~ greater_or_equal(A,start_time(sK0)) ),
inference(resolve,[status(thm)],[c_12,c_15]) ).
cnf(c_29,negated_conjecture,
greater(disbanding_rate(first_movers,initial_FM_EP(sK0)),disbanding_rate(efficient_producers,initial_FM_EP(sK0))),
inference(resolve,[status(thm)],[c_12,c_14]) ).
cnf(c_31,negated_conjecture,
~ greater(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)),
inference(split_conjunct,[status(thm)],[sk_prove_l2_neg]) ).
cnf(c_32,negated_conjecture,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_prove_l2_neg]) ).
cnf(c_33,plain,
( B = A
| greater(A,B)
| ~ greater_or_equal(A,B) ),
inference(clausify,[status(thm)],[mp_greater_or_equal]) ).
cnf(c_38,plain,
in_environment(sK0,sK1),
inference(resolve,[status(thm)],[c_32,c_26]) ).
cnf(c_80,negated_conjecture,
( greater(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))
| decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A)))
| ~ greater(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))
| ~ greater_or_equal(sK1,A)
| ~ greater_or_equal(A,B) ),
inference(resolve,[status(thm)],[c_32,c_25]) ).
cnf(c_39,negated_conjecture,
( decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A)))
| ~ greater(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B))
| ~ greater_or_equal(sK1,A)
| ~ greater_or_equal(A,B) ),
inference(resolve,[status(thm)],[c_31,c_80]) ).
cnf(c_40,plain,
greater_or_equal(sK1,initial_FM_EP(sK0)),
inference(resolve,[status(thm)],[c_32,c_24]) ).
cnf(c_41,plain,
~ decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))),
inference(resolve,[status(thm)],[c_32,c_22]) ).
cnf(c_46,plain,
( in_environment(sK0,A)
| ~ greater(sK1,A)
| ~ greater_or_equal(A,start_time(sK0)) ),
inference(resolve,[status(thm)],[c_38,c_28]) ).
cnf(c_47,plain,
( initial_FM_EP(sK0) = sK1
| greater(sK1,initial_FM_EP(sK0)) ),
inference(resolve,[status(thm)],[c_40,c_33]) ).
cnf(c_81,negated_conjecture,
( greater(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A))
| decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| ~ greater(disbanding_rate(first_movers,initial_FM_EP(sK0)),disbanding_rate(efficient_producers,initial_FM_EP(sK0)))
| ~ subpopulations(first_movers,efficient_producers,sK0,A)
| ~ greater_or_equal(A,sK1) ),
inference(resolve,[status(thm)],[c_25,c_40]) ).
cnf(c_82,negated_conjecture,
( greater(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))
| decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| ~ greater(disbanding_rate(first_movers,initial_FM_EP(sK0)),disbanding_rate(efficient_producers,initial_FM_EP(sK0)))
| ~ greater_or_equal(sK1,sK1) ),
inference(resolve,[status(thm)],[c_81,c_32]) ).
cnf(c_83,negated_conjecture,
( greater(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))
| decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)))
| ~ greater_or_equal(sK1,sK1) ),
inference(resolve,[status(thm)],[c_82,c_29]) ).
cnf(c_84,negated_conjecture,
( greater(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))
| ~ greater_or_equal(sK1,sK1) ),
inference(resolve,[status(thm)],[c_83,c_41]) ).
cnf(c_48,negated_conjecture,
~ greater_or_equal(sK1,sK1),
inference(resolve,[status(thm)],[c_84,c_31]) ).
cnf(c_53,plain,
( in_environment(sK0,initial_FM_EP(sK0))
| ~ greater(sK1,initial_FM_EP(sK0)) ),
inference(resolve,[status(thm)],[c_46,c_27]) ).
cnf(c_54,plain,
( initial_FM_EP(sK0) = sK1
| in_environment(sK0,initial_FM_EP(sK0)) ),
inference(resolve,[status(thm)],[c_53,c_47]) ).
cnf(c_56,plain,
( subpopulations(first_movers,efficient_producers,sK0,initial_FM_EP(sK0))
| initial_FM_EP(sK0) = sK1 ),
inference(resolve,[status(thm)],[c_54,c_23]) ).
cnf(c_62,plain,
( greater_or_equal(initial_FM_EP(sK0),initial_FM_EP(sK0))
| initial_FM_EP(sK0) = sK1 ),
inference(resolve,[status(thm)],[c_56,c_24]) ).
cnf(c_63,plain,
( ~ decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sK0)),disbanding_rate(efficient_producers,initial_FM_EP(sK0))))
| initial_FM_EP(sK0) = sK1 ),
inference(resolve,[status(thm)],[c_56,c_22]) ).
cnf(c_85,plain,
( decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sK0)),disbanding_rate(efficient_producers,initial_FM_EP(sK0))))
| ~ greater(disbanding_rate(first_movers,initial_FM_EP(sK0)),disbanding_rate(efficient_producers,initial_FM_EP(sK0)))
| ~ greater_or_equal(sK1,initial_FM_EP(sK0))
| initial_FM_EP(sK0) = sK1 ),
inference(resolve,[status(thm)],[c_62,c_39]) ).
cnf(c_86,plain,
( decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sK0)),disbanding_rate(efficient_producers,initial_FM_EP(sK0))))
| ~ greater(disbanding_rate(first_movers,initial_FM_EP(sK0)),disbanding_rate(efficient_producers,initial_FM_EP(sK0)))
| initial_FM_EP(sK0) = sK1 ),
inference(resolve,[status(thm)],[c_40,c_85]) ).
cnf(c_66,negated_conjecture,
( decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sK0)),disbanding_rate(efficient_producers,initial_FM_EP(sK0))))
| initial_FM_EP(sK0) = sK1 ),
inference(resolve,[status(thm)],[c_29,c_86]) ).
cnf(c_87,plain,
( initial_FM_EP(sK0) = sK1
| initial_FM_EP(sK0) = sK1 ),
inference(resolve,[status(thm)],[c_66,c_63]) ).
cnf(c_71,plain,
initial_FM_EP(sK0) = sK1,
inference(copy,[status(thm)],[c_87]) ).
cnf(c_88,plain,
greater_or_equal(sK1,sK1),
inference(paramod,[status(thm)],[c_71,c_40]) ).
cnf(c_79,plain,
$false,
inference(resolve,[status(thm)],[c_48,c_88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT020+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.57 % Computer : n004.cluster.edu
% 0.09/0.57 % Model : x86_64 x86_64
% 0.09/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.57 % Memory : 8046.5625MB
% 0.09/0.57 % OS : Linux 6.8.0-71-generic
% 0.09/0.57 % CPULimit : 300
% 0.09/0.57 % WCLimit : 300
% 0.09/0.57 % DateTime : Sat Sep 26 00:04:10 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.09/0.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.57 % Process 298751 was started by sandbox on n004,
% 0.09/0.57 % Sat Sep 26 00:04:10 2026
% 0.09/0.57 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.58
% 0.09/0.58 % From the command line: assign(max_seconds, 300).
% 0.09/0.59
% 0.09/0.59 % SZS status Theorem for theBenchmark
% 0.09/0.59
% 0.09/0.59 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.59 % Length of proof is 44.
% 0.09/0.59 % Level of proof is 11.
% 0.09/0.59 % Maximum clause weight is 33.000.
% 0.09/0.59 % Given clauses 40.
% 0.09/0.59
% 0.09/0.59 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------