%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT027-1 : 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 08:02:10 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.38s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 15
% Syntax : Number of formulae : 80 ( 19 unt; 0 def)
% Number of atoms : 213 ( 16 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 249 ( 116 ~; 133 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 67 ( 0 sgn 25 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_l9_37,axiom,
environment(sk3),
file('theBenchmark.p',prove_l9_37) ).
cnf(c_1,plain,
environment(sk3),
inference(clausify,[status(thm)],[prove_l9_37]) ).
fof(l10_36,axiom,
! [VAR_0,VAR_1] :
( greater(zero,growth_rate(first_movers,VAR_1))
| ~ greater_or_equal(VAR_1,sk2(VAR_0))
| ~ subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ stable(VAR_0)
| ~ environment(VAR_0) ),
file('theBenchmark.p',l10_36) ).
cnf(c_2,plain,
( greater(zero,growth_rate(first_movers,B))
| ~ greater_or_equal(B,sk2(A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l10_36]) ).
fof(l10_35,axiom,
! [VAR_0] :
( greater(sk2(VAR_0),appear(efficient_producers,VAR_0))
| ~ stable(VAR_0)
| ~ environment(VAR_0) ),
file('theBenchmark.p',l10_35) ).
cnf(c_3,plain,
( greater(sk2(A),appear(efficient_producers,A))
| ~ stable(A)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l10_35]) ).
fof(t6_34,axiom,
! [VAR_0,VAR_1] :
( greater(cardinality_at_time(efficient_producers,VAR_1),zero)
| ~ greater_or_equal(VAR_1,appear(efficient_producers,VAR_0))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',t6_34) ).
cnf(c_4,plain,
( greater(cardinality_at_time(efficient_producers,B),zero)
| ~ greater_or_equal(B,appear(efficient_producers,A))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[t6_34]) ).
fof(mp_EP_in_stable_environments_29,axiom,
! [VAR_0] :
( in_environment(VAR_0,appear(efficient_producers,VAR_0))
| ~ stable(VAR_0)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_EP_in_stable_environments_29) ).
cnf(c_5,plain,
( in_environment(A,appear(efficient_producers,A))
| ~ stable(A)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_EP_in_stable_environments_29]) ).
fof(mp_long_stable_environments_28,axiom,
! [VAR_0,VAR_1,VAR_2] :
( in_environment(VAR_0,VAR_2)
| ~ greater(VAR_2,VAR_1)
| ~ in_environment(VAR_0,VAR_1)
| ~ stable(VAR_0)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_long_stable_environments_28) ).
cnf(c_6,plain,
( in_environment(A,C)
| ~ greater(C,B)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_long_stable_environments_28]) ).
fof(mp_non_empty_fm_and_ep_27,axiom,
! [VAR_0,VAR_1] :
( subpopulations(first_movers,efficient_producers,VAR_0,VAR_1)
| ~ greater(cardinality_at_time(efficient_producers,VAR_1),zero)
| ~ greater(cardinality_at_time(first_movers,VAR_1),zero)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_non_empty_fm_and_ep_27) ).
cnf(c_7,plain,
( subpopulations(first_movers,efficient_producers,A,B)
| ~ greater(cardinality_at_time(efficient_producers,B),zero)
| ~ greater(cardinality_at_time(first_movers,B),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_non_empty_fm_and_ep_27]) ).
fof(mp_contracts_from_26,axiom,
! [VAR_0,VAR_1] :
( contracts_from(VAR_1,first_movers)
| ~ greater(zero,growth_rate(first_movers,sk1(VAR_1,VAR_0)))
| ~ in_environment(VAR_0,VAR_1)
| ~ stable(VAR_0)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_contracts_from_26) ).
cnf(c_8,plain,
( contracts_from(B,first_movers)
| ~ greater(zero,growth_rate(first_movers,sk1(B,A)))
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_contracts_from_26]) ).
fof(mp_contracts_from_25,axiom,
! [VAR_0,VAR_1] :
( contracts_from(VAR_1,first_movers)
| greater_or_equal(sk1(VAR_1,VAR_0),VAR_1)
| ~ in_environment(VAR_0,VAR_1)
| ~ stable(VAR_0)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_contracts_from_25) ).
cnf(c_9,plain,
( contracts_from(B,first_movers)
| greater_or_equal(sk1(B,A),B)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_contracts_from_25]) ).
fof(mp_contracts_from_24,axiom,
! [VAR_0,VAR_1] :
( contracts_from(VAR_1,first_movers)
| greater(cardinality_at_time(first_movers,sk1(VAR_1,VAR_0)),zero)
| ~ in_environment(VAR_0,VAR_1)
| ~ stable(VAR_0)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_contracts_from_24) ).
cnf(c_10,plain,
( contracts_from(B,first_movers)
| greater(cardinality_at_time(first_movers,sk1(B,A)),zero)
| ~ in_environment(A,B)
| ~ stable(A)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_contracts_from_24]) ).
cnf(c_11,plain,
( contracts_from(A,first_movers)
| greater(cardinality_at_time(first_movers,sk1(A,sk3)),zero)
| ~ in_environment(sk3,A)
| ~ stable(sk3) ),
inference(resolve,[status(thm)],[c_1,c_10]) ).
cnf(c_12,plain,
( contracts_from(A,first_movers)
| greater_or_equal(sk1(A,sk3),A)
| ~ in_environment(sk3,A)
| ~ stable(sk3) ),
inference(resolve,[status(thm)],[c_1,c_9]) ).
cnf(c_13,plain,
( contracts_from(A,first_movers)
| ~ greater(zero,growth_rate(first_movers,sk1(A,sk3)))
| ~ in_environment(sk3,A)
| ~ stable(sk3) ),
inference(resolve,[status(thm)],[c_1,c_8]) ).
cnf(c_14,plain,
( subpopulations(first_movers,efficient_producers,sk3,A)
| ~ greater(cardinality_at_time(efficient_producers,A),zero)
| ~ greater(cardinality_at_time(first_movers,A),zero)
| ~ in_environment(sk3,A) ),
inference(resolve,[status(thm)],[c_1,c_7]) ).
cnf(c_15,plain,
( in_environment(sk3,B)
| ~ greater(B,A)
| ~ in_environment(sk3,A)
| ~ stable(sk3) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_16,plain,
( in_environment(sk3,appear(efficient_producers,sk3))
| ~ stable(sk3) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_17,plain,
( greater(cardinality_at_time(efficient_producers,A),zero)
| ~ greater_or_equal(A,appear(efficient_producers,sk3))
| ~ in_environment(sk3,A) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_18,plain,
( greater(sk2(sk3),appear(efficient_producers,sk3))
| ~ stable(sk3) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_19,plain,
( greater(zero,growth_rate(first_movers,A))
| ~ greater_or_equal(A,sk2(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,A)
| ~ stable(sk3) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(prove_l9_39,axiom,
! [VAR_0] :
( ~ contracts_from(VAR_0,first_movers)
| ~ greater(VAR_0,appear(efficient_producers,sk3)) ),
file('theBenchmark.p',prove_l9_39) ).
cnf(c_20,plain,
( ~ contracts_from(A,first_movers)
| ~ greater(A,appear(efficient_producers,sk3)) ),
inference(clausify,[status(thm)],[prove_l9_39]) ).
fof(prove_l9_38,axiom,
stable(sk3),
file('theBenchmark.p',prove_l9_38) ).
cnf(c_21,plain,
stable(sk3),
inference(clausify,[status(thm)],[prove_l9_38]) ).
fof(mp_greater_or_equal_32,axiom,
! [VAR_0,VAR_1] :
( greater_or_equal(VAR_0,VAR_1)
| ~ greater(VAR_0,VAR_1) ),
file('theBenchmark.p',mp_greater_or_equal_32) ).
cnf(c_23,plain,
( greater_or_equal(A,B)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],[mp_greater_or_equal_32]) ).
fof(mp_greater_or_equal_31,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_31) ).
cnf(c_24,plain,
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
inference(clausify,[status(thm)],[mp_greater_or_equal_31]) ).
fof(mp_greater_transitivity_30,axiom,
! [VAR_0,VAR_1,VAR_2] :
( greater(VAR_0,VAR_2)
| ~ greater(VAR_1,VAR_2)
| ~ greater(VAR_0,VAR_1) ),
file('theBenchmark.p',mp_greater_transitivity_30) ).
cnf(c_25,plain,
( greater(A,C)
| ~ greater(B,C)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],[mp_greater_transitivity_30]) ).
cnf(c_26,plain,
( greater(zero,growth_rate(first_movers,A))
| ~ greater_or_equal(A,sk2(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,A) ),
inference(resolve,[status(thm)],[c_21,c_19]) ).
cnf(c_27,plain,
greater(sk2(sk3),appear(efficient_producers,sk3)),
inference(resolve,[status(thm)],[c_21,c_18]) ).
cnf(c_28,plain,
in_environment(sk3,appear(efficient_producers,sk3)),
inference(resolve,[status(thm)],[c_21,c_16]) ).
cnf(c_29,plain,
( in_environment(sk3,B)
| ~ greater(B,A)
| ~ in_environment(sk3,A) ),
inference(resolve,[status(thm)],[c_21,c_15]) ).
cnf(c_30,plain,
( contracts_from(A,first_movers)
| ~ greater(zero,growth_rate(first_movers,sk1(A,sk3)))
| ~ in_environment(sk3,A) ),
inference(resolve,[status(thm)],[c_21,c_13]) ).
cnf(c_31,plain,
( contracts_from(A,first_movers)
| greater_or_equal(sk1(A,sk3),A)
| ~ in_environment(sk3,A) ),
inference(resolve,[status(thm)],[c_21,c_12]) ).
cnf(c_32,plain,
( contracts_from(A,first_movers)
| greater(cardinality_at_time(first_movers,sk1(A,sk3)),zero)
| ~ in_environment(sk3,A) ),
inference(resolve,[status(thm)],[c_21,c_11]) ).
cnf(c_34,plain,
( greater(A,appear(efficient_producers,sk3))
| ~ greater(A,sk2(sk3)) ),
inference(resolve,[status(thm)],[c_27,c_25]) ).
cnf(c_36,plain,
greater_or_equal(sk2(sk3),appear(efficient_producers,sk3)),
inference(resolve,[status(thm)],[c_27,c_23]) ).
cnf(c_37,plain,
~ contracts_from(sk2(sk3),first_movers),
inference(resolve,[status(thm)],[c_20,c_27]) ).
cnf(c_39,plain,
( in_environment(sk3,A)
| ~ greater(A,appear(efficient_producers,sk3)) ),
inference(resolve,[status(thm)],[c_29,c_28]) ).
cnf(c_45,plain,
( greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero)
| ~ in_environment(sk3,sk2(sk3)) ),
inference(resolve,[status(thm)],[c_36,c_17]) ).
cnf(c_49,plain,
in_environment(sk3,sk2(sk3)),
inference(resolve,[status(thm)],[c_39,c_27]) ).
cnf(c_50,plain,
greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero),
inference(resolve,[status(thm)],[c_49,c_45]) ).
cnf(c_89,plain,
( contracts_from(sk2(sk3),first_movers)
| greater(cardinality_at_time(first_movers,sk1(sk2(sk3),sk3)),zero) ),
inference(resolve,[status(thm)],[c_49,c_32]) ).
cnf(c_51,plain,
greater(cardinality_at_time(first_movers,sk1(sk2(sk3),sk3)),zero),
inference(resolve,[status(thm)],[c_37,c_89]) ).
cnf(c_90,plain,
( contracts_from(sk2(sk3),first_movers)
| greater_or_equal(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(resolve,[status(thm)],[c_49,c_31]) ).
cnf(c_52,plain,
greater_or_equal(sk1(sk2(sk3),sk3),sk2(sk3)),
inference(resolve,[status(thm)],[c_37,c_90]) ).
cnf(c_91,plain,
( contracts_from(sk2(sk3),first_movers)
| ~ greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
inference(resolve,[status(thm)],[c_49,c_30]) ).
cnf(c_53,plain,
~ greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3))),
inference(resolve,[status(thm)],[c_37,c_91]) ).
cnf(c_54,plain,
( in_environment(sk3,A)
| ~ greater(A,sk2(sk3)) ),
inference(resolve,[status(thm)],[c_49,c_29]) ).
cnf(c_92,plain,
( subpopulations(first_movers,efficient_producers,sk3,sk2(sk3))
| ~ greater(cardinality_at_time(efficient_producers,sk2(sk3)),zero)
| ~ greater(cardinality_at_time(first_movers,sk2(sk3)),zero) ),
inference(resolve,[status(thm)],[c_49,c_14]) ).
cnf(c_55,plain,
( subpopulations(first_movers,efficient_producers,sk3,sk2(sk3))
| ~ greater(cardinality_at_time(first_movers,sk2(sk3)),zero) ),
inference(resolve,[status(thm)],[c_50,c_92]) ).
cnf(c_59,plain,
( sk1(sk2(sk3),sk3) = sk2(sk3)
| greater(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(resolve,[status(thm)],[c_52,c_24]) ).
cnf(c_93,plain,
( greater(zero,growth_rate(first_movers,sk1(sk2(sk3),sk3)))
| ~ subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) ),
inference(resolve,[status(thm)],[c_26,c_52]) ).
cnf(c_60,plain,
~ subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)),
inference(resolve,[status(thm)],[c_93,c_53]) ).
cnf(c_66,plain,
( in_environment(sk3,sk1(sk2(sk3),sk3))
| sk1(sk2(sk3),sk3) = sk2(sk3) ),
inference(resolve,[status(thm)],[c_59,c_54]) ).
cnf(c_67,plain,
( greater(sk1(sk2(sk3),sk3),appear(efficient_producers,sk3))
| sk1(sk2(sk3),sk3) = sk2(sk3) ),
inference(resolve,[status(thm)],[c_59,c_34]) ).
cnf(c_94,plain,
( subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3))
| ~ greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero)
| ~ greater(cardinality_at_time(first_movers,sk1(sk2(sk3),sk3)),zero)
| sk1(sk2(sk3),sk3) = sk2(sk3) ),
inference(resolve,[status(thm)],[c_66,c_14]) ).
cnf(c_95,plain,
( subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3))
| ~ greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero)
| sk1(sk2(sk3),sk3) = sk2(sk3) ),
inference(resolve,[status(thm)],[c_51,c_94]) ).
cnf(c_74,plain,
( ~ greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero)
| sk1(sk2(sk3),sk3) = sk2(sk3) ),
inference(resolve,[status(thm)],[c_60,c_95]) ).
cnf(c_77,plain,
( greater_or_equal(sk1(sk2(sk3),sk3),appear(efficient_producers,sk3))
| sk1(sk2(sk3),sk3) = sk2(sk3) ),
inference(resolve,[status(thm)],[c_67,c_23]) ).
cnf(c_78,plain,
( greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero)
| ~ in_environment(sk3,sk1(sk2(sk3),sk3))
| sk1(sk2(sk3),sk3) = sk2(sk3) ),
inference(resolve,[status(thm)],[c_77,c_17]) ).
cnf(c_96,plain,
( sk1(sk2(sk3),sk3) = sk2(sk3)
| greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero)
| sk1(sk2(sk3),sk3) = sk2(sk3) ),
inference(resolve,[status(thm)],[c_78,c_66]) ).
cnf(c_80,plain,
( greater(cardinality_at_time(efficient_producers,sk1(sk2(sk3),sk3)),zero)
| sk1(sk2(sk3),sk3) = sk2(sk3) ),
inference(copy,[status(thm)],[c_96]) ).
cnf(c_97,plain,
( sk1(sk2(sk3),sk3) = sk2(sk3)
| sk1(sk2(sk3),sk3) = sk2(sk3) ),
inference(resolve,[status(thm)],[c_80,c_74]) ).
cnf(c_81,plain,
sk1(sk2(sk3),sk3) = sk2(sk3),
inference(copy,[status(thm)],[c_97]) ).
cnf(c_85,plain,
~ subpopulations(first_movers,efficient_producers,sk3,sk2(sk3)),
inference(paramod,[status(thm)],[c_81,c_60]) ).
cnf(c_87,plain,
greater(cardinality_at_time(first_movers,sk2(sk3)),zero),
inference(paramod,[status(thm)],[c_81,c_51]) ).
cnf(c_98,plain,
subpopulations(first_movers,efficient_producers,sk3,sk2(sk3)),
inference(resolve,[status(thm)],[c_87,c_55]) ).
cnf(c_88,plain,
$false,
inference(resolve,[status(thm)],[c_85,c_98]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT027-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n019.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 26 00:05:04 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 4043849 was started by sandbox on n019,
% 0.08/0.36 % Sat Sep 26 00:05:04 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.08/0.38
% 0.08/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.38
% 0.08/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.08/0.38 % Length of proof is 55.
% 0.08/0.38 % Level of proof is 13.
% 0.08/0.38 % Maximum clause weight is 21.000.
% 0.08/0.38 % Given clauses 58.
% 0.08/0.38
% 0.08/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------