%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT020-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 : Unsatisfiable 0.16s 5.47s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 15 unt; 0 def)
% Number of atoms : 146 ( 14 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 167 ( 78 ~; 89 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 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 : 50 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_l2_33,axiom,
environment(sk1),
file('theBenchmark.p',prove_l2_33) ).
cnf(c_1,plain,
environment(sk1),
inference(clausify,[status(thm)],[prove_l2_33]) ).
fof(a8_31,axiom,
! [VAR_0] :
( greater(disbanding_rate(first_movers,initial_FM_EP(VAR_0)),disbanding_rate(efficient_producers,initial_FM_EP(VAR_0)))
| ~ environment(VAR_0) ),
file('theBenchmark.p',a8_31) ).
cnf(c_3,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_31]) ).
fof(mp_times_in_order_28,axiom,
! [VAR_0,VAR_1,VAR_2] :
( in_environment(VAR_0,VAR_1)
| ~ in_environment(VAR_0,VAR_2)
| ~ greater(VAR_2,VAR_1)
| ~ greater_or_equal(VAR_1,start_time(VAR_0))
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_times_in_order_28) ).
cnf(c_4,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_28]) ).
fof(mp_initial_time_27,axiom,
! [VAR_0] :
( greater_or_equal(initial_FM_EP(VAR_0),start_time(VAR_0))
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_initial_time_27) ).
cnf(c_5,plain,
( greater_or_equal(initial_FM_EP(A),start_time(A))
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_initial_time_27]) ).
fof(mp_time_point_occurs_26,axiom,
! [VAR_0,VAR_1] :
( in_environment(VAR_0,VAR_1)
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_time_point_occurs_26) ).
cnf(c_6,plain,
( in_environment(A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_time_point_occurs_26]) ).
fof(mp_positive_function_difference_25,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( greater(disbanding_rate(first_movers,VAR_3),disbanding_rate(efficient_producers,VAR_3))
| decreases(difference(disbanding_rate(first_movers,VAR_1),disbanding_rate(efficient_producers,VAR_1)))
| ~ greater(disbanding_rate(first_movers,VAR_2),disbanding_rate(efficient_producers,VAR_2))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_3)
| ~ greater_or_equal(VAR_3,VAR_1)
| ~ greater_or_equal(VAR_1,VAR_2)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_positive_function_difference_25) ).
cnf(c_7,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_25]) ).
fof(mp_earliest_time_point_24,axiom,
! [VAR_0,VAR_1] :
( greater_or_equal(VAR_1,initial_FM_EP(VAR_0))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_earliest_time_point_24) ).
cnf(c_8,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_24]) ).
fof(mp_earliest_time_point_23,axiom,
! [VAR_0] :
( subpopulations(first_movers,efficient_producers,VAR_0,initial_FM_EP(VAR_0))
| ~ in_environment(VAR_0,initial_FM_EP(VAR_0))
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_earliest_time_point_23) ).
cnf(c_9,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_23]) ).
fof(l3_22,axiom,
! [VAR_0,VAR_1] :
( ~ decreases(difference(disbanding_rate(first_movers,VAR_1),disbanding_rate(efficient_producers,VAR_1)))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',l3_22) ).
cnf(c_10,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_22]) ).
cnf(c_11,plain,
( ~ decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A)))
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_12,plain,
( subpopulations(first_movers,efficient_producers,sk1,initial_FM_EP(sk1))
| ~ in_environment(sk1,initial_FM_EP(sk1)) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_13,plain,
( greater_or_equal(A,initial_FM_EP(sk1))
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_14,plain,
( 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,sk1,C)
| ~ greater_or_equal(C,A)
| ~ greater_or_equal(A,B) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_15,plain,
( in_environment(sk1,A)
| ~ subpopulations(first_movers,efficient_producers,sk1,A) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_16,plain,
greater_or_equal(initial_FM_EP(sk1),start_time(sk1)),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_17,plain,
( in_environment(sk1,A)
| ~ in_environment(sk1,B)
| ~ greater(B,A)
| ~ greater_or_equal(A,start_time(sk1)) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_18,plain,
greater(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1))),
inference(resolve,[status(thm)],[c_1,c_3]) ).
fof(prove_l2_35,axiom,
~ greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)),
file('theBenchmark.p',prove_l2_35) ).
cnf(c_20,plain,
~ greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)),
inference(clausify,[status(thm)],[prove_l2_35]) ).
fof(prove_l2_34,axiom,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('theBenchmark.p',prove_l2_34) ).
cnf(c_21,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(clausify,[status(thm)],[prove_l2_34]) ).
fof(mp_greater_or_equal_30,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| greater(VAR_0,VAR_1)
| ~ greater_or_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',mp_greater_or_equal_30) ).
cnf(c_22,plain,
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
inference(clausify,[status(thm)],[mp_greater_or_equal_30]) ).
cnf(c_27,plain,
in_environment(sk1,sk2),
inference(resolve,[status(thm)],[c_21,c_15]) ).
cnf(c_67,plain,
( greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))
| 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(sk2,A)
| ~ greater_or_equal(A,B) ),
inference(resolve,[status(thm)],[c_21,c_14]) ).
cnf(c_28,plain,
( 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(sk2,A)
| ~ greater_or_equal(A,B) ),
inference(resolve,[status(thm)],[c_20,c_67]) ).
cnf(c_29,plain,
greater_or_equal(sk2,initial_FM_EP(sk1)),
inference(resolve,[status(thm)],[c_21,c_13]) ).
cnf(c_30,plain,
~ decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))),
inference(resolve,[status(thm)],[c_21,c_11]) ).
cnf(c_35,plain,
( in_environment(sk1,A)
| ~ greater(sk2,A)
| ~ greater_or_equal(A,start_time(sk1)) ),
inference(resolve,[status(thm)],[c_27,c_17]) ).
cnf(c_68,plain,
( sk2 = initial_FM_EP(sk1)
| greater(sk2,initial_FM_EP(sk1)) ),
inference(resolve,[status(thm)],[c_29,c_22]) ).
cnf(c_36,plain,
( initial_FM_EP(sk1) = sk2
| greater(sk2,initial_FM_EP(sk1)) ),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_69,plain,
( greater(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A))
| decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ greater(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1)))
| ~ subpopulations(first_movers,efficient_producers,sk1,A)
| ~ greater_or_equal(A,sk2) ),
inference(resolve,[status(thm)],[c_14,c_29]) ).
cnf(c_70,plain,
( greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))
| decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ greater(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1)))
| ~ greater_or_equal(sk2,sk2) ),
inference(resolve,[status(thm)],[c_69,c_21]) ).
cnf(c_71,plain,
( greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))
| decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)))
| ~ greater_or_equal(sk2,sk2) ),
inference(resolve,[status(thm)],[c_70,c_18]) ).
cnf(c_72,plain,
( greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))
| ~ greater_or_equal(sk2,sk2) ),
inference(resolve,[status(thm)],[c_71,c_30]) ).
cnf(c_37,plain,
~ greater_or_equal(sk2,sk2),
inference(resolve,[status(thm)],[c_72,c_20]) ).
cnf(c_43,plain,
( in_environment(sk1,initial_FM_EP(sk1))
| ~ greater(sk2,initial_FM_EP(sk1)) ),
inference(resolve,[status(thm)],[c_35,c_16]) ).
cnf(c_46,plain,
( initial_FM_EP(sk1) = sk2
| in_environment(sk1,initial_FM_EP(sk1)) ),
inference(resolve,[status(thm)],[c_43,c_36]) ).
cnf(c_48,plain,
( subpopulations(first_movers,efficient_producers,sk1,initial_FM_EP(sk1))
| initial_FM_EP(sk1) = sk2 ),
inference(resolve,[status(thm)],[c_46,c_12]) ).
cnf(c_54,plain,
( greater_or_equal(initial_FM_EP(sk1),initial_FM_EP(sk1))
| initial_FM_EP(sk1) = sk2 ),
inference(resolve,[status(thm)],[c_48,c_13]) ).
cnf(c_55,plain,
( ~ decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1))))
| initial_FM_EP(sk1) = sk2 ),
inference(resolve,[status(thm)],[c_48,c_11]) ).
cnf(c_73,plain,
( decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1))))
| ~ greater(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1)))
| ~ greater_or_equal(sk2,initial_FM_EP(sk1))
| initial_FM_EP(sk1) = sk2 ),
inference(resolve,[status(thm)],[c_54,c_28]) ).
cnf(c_74,plain,
( decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1))))
| ~ greater(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1)))
| initial_FM_EP(sk1) = sk2 ),
inference(resolve,[status(thm)],[c_29,c_73]) ).
cnf(c_56,plain,
( decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1))))
| initial_FM_EP(sk1) = sk2 ),
inference(resolve,[status(thm)],[c_18,c_74]) ).
cnf(c_75,plain,
( initial_FM_EP(sk1) = sk2
| initial_FM_EP(sk1) = sk2 ),
inference(resolve,[status(thm)],[c_56,c_55]) ).
cnf(c_62,plain,
initial_FM_EP(sk1) = sk2,
inference(copy,[status(thm)],[c_75]) ).
cnf(c_76,plain,
greater_or_equal(sk2,sk2),
inference(paramod,[status(thm)],[c_62,c_29]) ).
cnf(c_66,plain,
$false,
inference(resolve,[status(thm)],[c_37,c_76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : MGT020-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/5.44 % Computer : n019.cluster.edu
% 0.16/5.44 % Model : x86_64 x86_64
% 0.16/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/5.44 % Memory : 8046.5625MB
% 0.16/5.44 % OS : Linux 6.8.0-71-generic
% 0.16/5.44 % CPULimit : 300
% 0.16/5.44 % WCLimit : 300
% 0.16/5.44 % DateTime : Sat Sep 26 00:04:11 UTC 2026
% 0.16/5.45 % CPUTime :
% 0.16/5.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.16/5.45 % Process 4040711 was started by sandbox on n019,
% 0.16/5.45 % Sat Sep 26 00:04:11 2026
% 0.16/5.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.16/5.46
% 0.16/5.46 % From the command line: assign(max_seconds, 300).
% 0.16/5.47
% 0.16/5.47 % SZS status Unsatisfiable for theBenchmark
% 0.16/5.47
% 0.16/5.47 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.16/5.47 % Length of proof is 35.
% 0.16/5.47 % Level of proof is 10.
% 0.16/5.47 % Maximum clause weight is 48.000.
% 0.16/5.47 % Given clauses 52.
% 0.16/5.47
% 0.16/5.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------