%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT039-1 : 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 : n020.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 08:02:55 AM UTC 2026
% Result : Unsatisfiable 0.08s 0.54s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 18
% Syntax : Number of formulae : 103 ( 21 unt; 0 def)
% Number of atoms : 301 ( 34 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 344 ( 146 ~; 198 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 63 ( 0 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_t8_36,axiom,
observational_period(sk3),
file('theBenchmark.p',prove_t8_36) ).
cnf(c_1,plain,
observational_period(sk3),
inference(clausify,[status(thm)],[prove_t8_36]) ).
fof(mp4_critical_point_24,axiom,
! [VAR_0,VAR_1] :
( greater(sk2(VAR_1,VAR_0),critical_point(VAR_1))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_1)
| ~ slow_change(VAR_0)
| ~ observational_period(VAR_0) ),
file('theBenchmark.p',mp4_critical_point_24) ).
cnf(c_2,plain,
( greater(sk2(B,A),critical_point(B))
| ~ in_environment(A,B)
| ~ environment(B)
| ~ slow_change(A)
| ~ observational_period(A) ),
inference(clausify,[status(thm)],[mp4_critical_point_24]) ).
fof(mp4_critical_point_23,axiom,
! [VAR_0,VAR_1] :
( in_environment(VAR_1,sk2(VAR_1,VAR_0))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_1)
| ~ slow_change(VAR_0)
| ~ observational_period(VAR_0) ),
file('theBenchmark.p',mp4_critical_point_23) ).
cnf(c_3,plain,
( in_environment(B,sk2(B,A))
| ~ in_environment(A,B)
| ~ environment(B)
| ~ slow_change(A)
| ~ observational_period(A) ),
inference(clausify,[status(thm)],[mp4_critical_point_23]) ).
fof(mp3_favoured_trategy_22,axiom,
! [VAR_0] :
( selection_favors(efficient_producers,first_movers,VAR_0)
| ~ selection_favors(efficient_producers,first_movers,end_time(sk1(VAR_0)))
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(VAR_0) ),
file('theBenchmark.p',mp3_favoured_trategy_22) ).
cnf(c_4,plain,
( selection_favors(efficient_producers,first_movers,A)
| ~ selection_favors(efficient_producers,first_movers,end_time(sk1(A)))
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(A) ),
inference(clausify,[status(thm)],[mp3_favoured_trategy_22]) ).
fof(mp3_favoured_trategy_21,axiom,
! [VAR_0] :
( selection_favors(efficient_producers,first_movers,VAR_0)
| in_environment(VAR_0,sk1(VAR_0))
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(VAR_0) ),
file('theBenchmark.p',mp3_favoured_trategy_21) ).
cnf(c_5,plain,
( selection_favors(efficient_producers,first_movers,A)
| in_environment(A,sk1(A))
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(A) ),
inference(clausify,[status(thm)],[mp3_favoured_trategy_21]) ).
fof(mp3_favoured_trategy_20,axiom,
! [VAR_0] :
( selection_favors(efficient_producers,first_movers,VAR_0)
| environment(sk1(VAR_0))
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(VAR_0) ),
file('theBenchmark.p',mp3_favoured_trategy_20) ).
cnf(c_6,plain,
( selection_favors(efficient_producers,first_movers,A)
| environment(sk1(A))
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(A) ),
inference(clausify,[status(thm)],[mp3_favoured_trategy_20]) ).
cnf(c_7,plain,
( in_environment(A,sk2(A,sk3))
| ~ in_environment(sk3,A)
| ~ environment(A)
| ~ slow_change(sk3) ),
inference(resolve,[status(thm)],[c_1,c_3]) ).
cnf(c_8,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| environment(sk1(sk3))
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers) ),
inference(resolve,[status(thm)],[c_1,c_6]) ).
cnf(c_9,plain,
( greater(sk2(A,sk3),critical_point(A))
| ~ in_environment(sk3,A)
| ~ environment(A)
| ~ slow_change(sk3) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(l8_35,axiom,
! [VAR_0,VAR_1] :
( selection_favors(efficient_producers,first_movers,VAR_1)
| ~ greater(VAR_1,critical_point(VAR_0))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',l8_35) ).
cnf(c_10,plain,
( selection_favors(efficient_producers,first_movers,B)
| ~ greater(B,critical_point(A))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l8_35]) ).
fof(mp_time_of_critical_point_29,axiom,
! [VAR_0] :
( greater_or_equal(critical_point(VAR_0),start_time(VAR_0))
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_time_of_critical_point_29) ).
cnf(c_12,plain,
( greater_or_equal(critical_point(A),start_time(A))
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_time_of_critical_point_29]) ).
fof(mp_environment_end_point_28,axiom,
! [VAR_0,VAR_1] :
( greater_or_equal(end_time(VAR_0),VAR_1)
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_environment_end_point_28) ).
cnf(c_13,plain,
( greater_or_equal(end_time(A),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_environment_end_point_28]) ).
fof(mp_time_in_environment_27,axiom,
! [VAR_0,VAR_1] :
( in_environment(VAR_0,VAR_1)
| ~ greater_or_equal(end_time(VAR_0),VAR_1)
| ~ greater_or_equal(VAR_1,start_time(VAR_0))
| ~ environment(VAR_0) ),
file('theBenchmark.p',mp_time_in_environment_27) ).
cnf(c_14,plain,
( in_environment(A,B)
| ~ greater_or_equal(end_time(A),B)
| ~ greater_or_equal(B,start_time(A))
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_time_in_environment_27]) ).
cnf(c_15,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| in_environment(sk1(sk3),A)
| ~ greater_or_equal(end_time(sk1(sk3)),A)
| ~ greater_or_equal(A,start_time(sk1(sk3))) ),
inference(resolve,[status(thm)],[c_14,c_8]) ).
cnf(c_16,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| greater_or_equal(end_time(sk1(sk3)),A)
| ~ in_environment(sk1(sk3),A) ),
inference(resolve,[status(thm)],[c_13,c_8]) ).
cnf(c_17,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| greater_or_equal(critical_point(sk1(sk3)),start_time(sk1(sk3))) ),
inference(resolve,[status(thm)],[c_12,c_8]) ).
cnf(c_19,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| selection_favors(efficient_producers,first_movers,A)
| ~ greater(A,critical_point(sk1(sk3)))
| ~ in_environment(sk1(sk3),A) ),
inference(resolve,[status(thm)],[c_10,c_8]) ).
cnf(c_20,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| greater(sk2(sk1(sk3),sk3),critical_point(sk1(sk3)))
| ~ in_environment(sk3,sk1(sk3))
| ~ slow_change(sk3) ),
inference(resolve,[status(thm)],[c_9,c_8]) ).
cnf(c_21,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| in_environment(sk1(sk3),sk2(sk1(sk3),sk3))
| ~ in_environment(sk3,sk1(sk3))
| ~ slow_change(sk3) ),
inference(resolve,[status(thm)],[c_7,c_8]) ).
fof(mp_organizational_sets1_25,axiom,
propagation_strategy(first_movers),
file('theBenchmark.p',mp_organizational_sets1_25) ).
cnf(c_22,plain,
propagation_strategy(first_movers),
inference(clausify,[status(thm)],[mp_organizational_sets1_25]) ).
fof(mp_organizational_sets2_26,axiom,
propagation_strategy(efficient_producers),
file('theBenchmark.p',mp_organizational_sets2_26) ).
cnf(c_23,plain,
propagation_strategy(efficient_producers),
inference(clausify,[status(thm)],[mp_organizational_sets2_26]) ).
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_24,plain,
( greater(A,C)
| ~ greater(B,C)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],[mp_greater_transitivity_30]) ).
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_25,plain,
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
inference(clausify,[status(thm)],[mp_greater_or_equal_31]) ).
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_26,plain,
( greater_or_equal(A,B)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],[mp_greater_or_equal_32]) ).
fof(mp_greater_or_equal_33,axiom,
! [VAR_0,VAR_1] :
( greater_or_equal(VAR_0,VAR_1)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',mp_greater_or_equal_33) ).
cnf(c_27,plain,
( greater_or_equal(A,B)
| A != B ),
inference(clausify,[status(thm)],[mp_greater_or_equal_33]) ).
fof(prove_t8_37,axiom,
slow_change(sk3),
file('theBenchmark.p',prove_t8_37) ).
cnf(c_28,plain,
slow_change(sk3),
inference(clausify,[status(thm)],[prove_t8_37]) ).
fof(prove_t8_38,axiom,
~ selection_favors(efficient_producers,first_movers,sk3),
file('theBenchmark.p',prove_t8_38) ).
cnf(c_29,plain,
~ selection_favors(efficient_producers,first_movers,sk3),
inference(clausify,[status(thm)],[prove_t8_38]) ).
cnf(c_30,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ selection_favors(efficient_producers,first_movers,end_time(sk1(sk3)))
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers) ),
inference(resolve,[status(thm)],[c_1,c_4]) ).
cnf(c_100,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ selection_favors(efficient_producers,first_movers,end_time(sk1(sk3)))
| ~ propagation_strategy(efficient_producers) ),
inference(resolve,[status(thm)],[c_22,c_30]) ).
cnf(c_101,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ selection_favors(efficient_producers,first_movers,end_time(sk1(sk3))) ),
inference(resolve,[status(thm)],[c_23,c_100]) ).
cnf(c_31,plain,
~ selection_favors(efficient_producers,first_movers,end_time(sk1(sk3))),
inference(resolve,[status(thm)],[c_29,c_101]) ).
cnf(c_32,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| in_environment(sk3,sk1(sk3))
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers) ),
inference(resolve,[status(thm)],[c_1,c_5]) ).
cnf(c_102,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| in_environment(sk3,sk1(sk3))
| ~ propagation_strategy(efficient_producers) ),
inference(resolve,[status(thm)],[c_22,c_32]) ).
cnf(c_103,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| in_environment(sk3,sk1(sk3)) ),
inference(resolve,[status(thm)],[c_23,c_102]) ).
cnf(c_33,plain,
in_environment(sk3,sk1(sk3)),
inference(resolve,[status(thm)],[c_29,c_103]) ).
cnf(c_104,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| in_environment(sk1(sk3),sk2(sk1(sk3),sk3))
| ~ in_environment(sk3,sk1(sk3)) ),
inference(resolve,[status(thm)],[c_28,c_21]) ).
cnf(c_105,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| in_environment(sk1(sk3),sk2(sk1(sk3),sk3)) ),
inference(resolve,[status(thm)],[c_33,c_104]) ).
cnf(c_106,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ propagation_strategy(efficient_producers)
| in_environment(sk1(sk3),sk2(sk1(sk3),sk3)) ),
inference(resolve,[status(thm)],[c_22,c_105]) ).
cnf(c_107,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| in_environment(sk1(sk3),sk2(sk1(sk3),sk3)) ),
inference(resolve,[status(thm)],[c_23,c_106]) ).
cnf(c_35,plain,
in_environment(sk1(sk3),sk2(sk1(sk3),sk3)),
inference(resolve,[status(thm)],[c_29,c_107]) ).
cnf(c_108,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| greater(sk2(sk1(sk3),sk3),critical_point(sk1(sk3)))
| ~ in_environment(sk3,sk1(sk3)) ),
inference(resolve,[status(thm)],[c_28,c_20]) ).
cnf(c_109,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| greater(sk2(sk1(sk3),sk3),critical_point(sk1(sk3))) ),
inference(resolve,[status(thm)],[c_33,c_108]) ).
cnf(c_110,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ propagation_strategy(efficient_producers)
| greater(sk2(sk1(sk3),sk3),critical_point(sk1(sk3))) ),
inference(resolve,[status(thm)],[c_22,c_109]) ).
cnf(c_111,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| greater(sk2(sk1(sk3),sk3),critical_point(sk1(sk3))) ),
inference(resolve,[status(thm)],[c_23,c_110]) ).
cnf(c_36,plain,
greater(sk2(sk1(sk3),sk3),critical_point(sk1(sk3))),
inference(resolve,[status(thm)],[c_29,c_111]) ).
cnf(c_112,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ propagation_strategy(efficient_producers)
| selection_favors(efficient_producers,first_movers,A)
| ~ greater(A,critical_point(sk1(sk3)))
| ~ in_environment(sk1(sk3),A) ),
inference(resolve,[status(thm)],[c_22,c_19]) ).
cnf(c_113,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| selection_favors(efficient_producers,first_movers,A)
| ~ greater(A,critical_point(sk1(sk3)))
| ~ in_environment(sk1(sk3),A) ),
inference(resolve,[status(thm)],[c_23,c_112]) ).
cnf(c_37,plain,
( selection_favors(efficient_producers,first_movers,A)
| ~ greater(A,critical_point(sk1(sk3)))
| ~ in_environment(sk1(sk3),A) ),
inference(resolve,[status(thm)],[c_29,c_113]) ).
cnf(c_114,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ propagation_strategy(efficient_producers)
| greater_or_equal(critical_point(sk1(sk3)),start_time(sk1(sk3))) ),
inference(resolve,[status(thm)],[c_22,c_17]) ).
cnf(c_115,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| greater_or_equal(critical_point(sk1(sk3)),start_time(sk1(sk3))) ),
inference(resolve,[status(thm)],[c_23,c_114]) ).
cnf(c_39,plain,
greater_or_equal(critical_point(sk1(sk3)),start_time(sk1(sk3))),
inference(resolve,[status(thm)],[c_29,c_115]) ).
cnf(c_116,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ propagation_strategy(efficient_producers)
| greater_or_equal(end_time(sk1(sk3)),A)
| ~ in_environment(sk1(sk3),A) ),
inference(resolve,[status(thm)],[c_22,c_16]) ).
cnf(c_117,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| greater_or_equal(end_time(sk1(sk3)),A)
| ~ in_environment(sk1(sk3),A) ),
inference(resolve,[status(thm)],[c_23,c_116]) ).
cnf(c_40,plain,
( greater_or_equal(end_time(sk1(sk3)),A)
| ~ in_environment(sk1(sk3),A) ),
inference(resolve,[status(thm)],[c_29,c_117]) ).
cnf(c_118,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| ~ propagation_strategy(efficient_producers)
| in_environment(sk1(sk3),A)
| ~ greater_or_equal(end_time(sk1(sk3)),A)
| ~ greater_or_equal(A,start_time(sk1(sk3))) ),
inference(resolve,[status(thm)],[c_22,c_15]) ).
cnf(c_119,plain,
( selection_favors(efficient_producers,first_movers,sk3)
| in_environment(sk1(sk3),A)
| ~ greater_or_equal(end_time(sk1(sk3)),A)
| ~ greater_or_equal(A,start_time(sk1(sk3))) ),
inference(resolve,[status(thm)],[c_23,c_118]) ).
cnf(c_41,plain,
( in_environment(sk1(sk3),A)
| ~ greater_or_equal(end_time(sk1(sk3)),A)
| ~ greater_or_equal(A,start_time(sk1(sk3))) ),
inference(resolve,[status(thm)],[c_29,c_119]) ).
cnf(c_42,plain,
greater_or_equal(A,A),
inference(xxres,[status(thm)],[c_27]) ).
cnf(c_44,plain,
( greater(A,critical_point(sk1(sk3)))
| ~ greater(A,sk2(sk1(sk3),sk3)) ),
inference(resolve,[status(thm)],[c_36,c_24]) ).
cnf(c_120,plain,
( selection_favors(efficient_producers,first_movers,sk2(sk1(sk3),sk3))
| ~ greater(sk2(sk1(sk3),sk3),critical_point(sk1(sk3))) ),
inference(resolve,[status(thm)],[c_37,c_35]) ).
cnf(c_46,plain,
selection_favors(efficient_producers,first_movers,sk2(sk1(sk3),sk3)),
inference(resolve,[status(thm)],[c_36,c_120]) ).
cnf(c_121,plain,
( critical_point(sk1(sk3)) = start_time(sk1(sk3))
| greater(critical_point(sk1(sk3)),start_time(sk1(sk3))) ),
inference(resolve,[status(thm)],[c_39,c_25]) ).
cnf(c_47,plain,
( start_time(sk1(sk3)) = critical_point(sk1(sk3))
| greater(critical_point(sk1(sk3)),start_time(sk1(sk3))) ),
inference(copy,[status(thm)],[c_121]) ).
cnf(c_48,plain,
greater_or_equal(end_time(sk1(sk3)),sk2(sk1(sk3),sk3)),
inference(resolve,[status(thm)],[c_40,c_35]) ).
cnf(c_50,plain,
( in_environment(sk1(sk3),end_time(sk1(sk3)))
| ~ greater_or_equal(end_time(sk1(sk3)),start_time(sk1(sk3))) ),
inference(resolve,[status(thm)],[c_42,c_41]) ).
cnf(c_52,plain,
( end_time(sk1(sk3)) = sk2(sk1(sk3),sk3)
| greater(end_time(sk1(sk3)),sk2(sk1(sk3),sk3)) ),
inference(resolve,[status(thm)],[c_48,c_25]) ).
cnf(c_55,plain,
( greater(A,start_time(sk1(sk3)))
| ~ greater(A,critical_point(sk1(sk3)))
| start_time(sk1(sk3)) = critical_point(sk1(sk3)) ),
inference(resolve,[status(thm)],[c_47,c_24]) ).
cnf(c_57,plain,
( greater(end_time(sk1(sk3)),critical_point(sk1(sk3)))
| end_time(sk1(sk3)) = sk2(sk1(sk3),sk3) ),
inference(resolve,[status(thm)],[c_52,c_44]) ).
cnf(c_63,plain,
( greater_or_equal(end_time(sk1(sk3)),critical_point(sk1(sk3)))
| end_time(sk1(sk3)) = sk2(sk1(sk3),sk3) ),
inference(resolve,[status(thm)],[c_57,c_26]) ).
cnf(c_70,plain,
( end_time(sk1(sk3)) = sk2(sk1(sk3),sk3)
| greater(end_time(sk1(sk3)),start_time(sk1(sk3)))
| start_time(sk1(sk3)) = critical_point(sk1(sk3)) ),
inference(resolve,[status(thm)],[c_55,c_57]) ).
cnf(c_72,plain,
( greater_or_equal(end_time(sk1(sk3)),start_time(sk1(sk3)))
| end_time(sk1(sk3)) = sk2(sk1(sk3),sk3)
| start_time(sk1(sk3)) = critical_point(sk1(sk3)) ),
inference(resolve,[status(thm)],[c_70,c_26]) ).
cnf(c_76,plain,
( in_environment(sk1(sk3),end_time(sk1(sk3)))
| end_time(sk1(sk3)) = sk2(sk1(sk3),sk3)
| start_time(sk1(sk3)) = critical_point(sk1(sk3)) ),
inference(resolve,[status(thm)],[c_72,c_50]) ).
cnf(c_122,plain,
( selection_favors(efficient_producers,first_movers,end_time(sk1(sk3)))
| ~ greater(end_time(sk1(sk3)),critical_point(sk1(sk3)))
| end_time(sk1(sk3)) = sk2(sk1(sk3),sk3)
| start_time(sk1(sk3)) = critical_point(sk1(sk3)) ),
inference(resolve,[status(thm)],[c_76,c_37]) ).
cnf(c_82,plain,
( ~ greater(end_time(sk1(sk3)),critical_point(sk1(sk3)))
| end_time(sk1(sk3)) = sk2(sk1(sk3),sk3)
| start_time(sk1(sk3)) = critical_point(sk1(sk3)) ),
inference(resolve,[status(thm)],[c_31,c_122]) ).
cnf(c_123,plain,
( end_time(sk1(sk3)) = sk2(sk1(sk3),sk3)
| end_time(sk1(sk3)) = sk2(sk1(sk3),sk3)
| start_time(sk1(sk3)) = critical_point(sk1(sk3)) ),
inference(resolve,[status(thm)],[c_82,c_57]) ).
cnf(c_83,plain,
( end_time(sk1(sk3)) = sk2(sk1(sk3),sk3)
| start_time(sk1(sk3)) = critical_point(sk1(sk3)) ),
inference(copy,[status(thm)],[c_123]) ).
cnf(c_87,plain,
( in_environment(sk1(sk3),end_time(sk1(sk3)))
| ~ greater_or_equal(end_time(sk1(sk3)),critical_point(sk1(sk3)))
| end_time(sk1(sk3)) = sk2(sk1(sk3),sk3) ),
inference(paramod,[status(thm)],[c_83,c_50]) ).
cnf(c_124,plain,
( end_time(sk1(sk3)) = sk2(sk1(sk3),sk3)
| in_environment(sk1(sk3),end_time(sk1(sk3)))
| end_time(sk1(sk3)) = sk2(sk1(sk3),sk3) ),
inference(resolve,[status(thm)],[c_87,c_63]) ).
cnf(c_89,plain,
( in_environment(sk1(sk3),end_time(sk1(sk3)))
| end_time(sk1(sk3)) = sk2(sk1(sk3),sk3) ),
inference(copy,[status(thm)],[c_124]) ).
cnf(c_125,plain,
( selection_favors(efficient_producers,first_movers,end_time(sk1(sk3)))
| ~ greater(end_time(sk1(sk3)),critical_point(sk1(sk3)))
| end_time(sk1(sk3)) = sk2(sk1(sk3),sk3) ),
inference(resolve,[status(thm)],[c_89,c_37]) ).
cnf(c_90,plain,
( ~ greater(end_time(sk1(sk3)),critical_point(sk1(sk3)))
| end_time(sk1(sk3)) = sk2(sk1(sk3),sk3) ),
inference(resolve,[status(thm)],[c_31,c_125]) ).
cnf(c_126,plain,
( end_time(sk1(sk3)) = sk2(sk1(sk3),sk3)
| end_time(sk1(sk3)) = sk2(sk1(sk3),sk3) ),
inference(resolve,[status(thm)],[c_90,c_57]) ).
cnf(c_91,plain,
end_time(sk1(sk3)) = sk2(sk1(sk3),sk3),
inference(copy,[status(thm)],[c_126]) ).
cnf(c_127,plain,
~ selection_favors(efficient_producers,first_movers,sk2(sk1(sk3),sk3)),
inference(paramod,[status(thm)],[c_91,c_31]) ).
cnf(c_99,plain,
$false,
inference(resolve,[status(thm)],[c_46,c_127]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT039-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.52 % Computer : n020.cluster.edu
% 0.08/0.52 % Model : x86_64 x86_64
% 0.08/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.52 % Memory : 8046.5625MB
% 0.08/0.52 % OS : Linux 6.8.0-71-generic
% 0.08/0.52 % CPULimit : 300
% 0.08/0.52 % WCLimit : 300
% 0.08/0.52 % DateTime : Sat Sep 26 00:07:50 UTC 2026
% 0.08/0.52 % CPUTime :
% 0.08/0.52 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.52 % Process 4156676 was started by sandbox on n020,
% 0.08/0.52 % Sat Sep 26 00:07:50 2026
% 0.08/0.52 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.53
% 0.08/0.53 % From the command line: assign(max_seconds, 300).
% 0.08/0.54
% 0.08/0.54 % SZS status Unsatisfiable for theBenchmark
% 0.08/0.54
% 0.08/0.54 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.08/0.54 % Length of proof is 57.
% 0.08/0.54 % Level of proof is 16.
% 0.08/0.54 % Maximum clause weight is 22.000.
% 0.08/0.54 % Given clauses 57.
% 0.08/0.54
% 0.08/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------