%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : MGT039+1 : 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 : 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 08:02:55 AM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 11
% Syntax : Number of formulae : 105 ( 18 unt; 0 def)
% Number of atoms : 345 ( 33 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 390 ( 150 ~; 200 |; 28 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 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 : 75 ( 0 sgn 31 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp3_favoured_trategy,axiom,
! [P] :
( ( ! [E] :
( ( in_environment(P,E)
& environment(E) )
=> selection_favors(efficient_producers,first_movers,end_time(E)) )
& propagation_strategy(efficient_producers)
& propagation_strategy(first_movers)
& observational_period(P) )
=> selection_favors(efficient_producers,first_movers,P) ),
file('theBenchmark.p',mp3_favoured_trategy) ).
fof(mp4_critical_point,axiom,
! [P] :
( ( slow_change(P)
& observational_period(P) )
=> ! [E] :
( ( in_environment(P,E)
& environment(E) )
=> ? [T] :
( greater(T,critical_point(E))
& in_environment(E,T) ) ) ),
file('theBenchmark.p',mp4_critical_point) ).
fof(mp_time_in_environment,axiom,
! [E,T] :
( ( greater_or_equal(end_time(E),T)
& greater_or_equal(T,start_time(E))
& environment(E) )
=> in_environment(E,T) ),
file('theBenchmark.p',mp_time_in_environment) ).
fof(mp_environment_end_point,axiom,
! [E,T] :
( ( in_environment(E,T)
& environment(E) )
=> greater_or_equal(end_time(E),T) ),
file('theBenchmark.p',mp_environment_end_point) ).
fof(mp_time_of_critical_point,axiom,
! [E] :
( environment(E)
=> greater_or_equal(critical_point(E),start_time(E)) ),
file('theBenchmark.p',mp_time_of_critical_point) ).
fof(mp_greater_transitivity,axiom,
! [X,Y,Z] :
( ( greater(Y,Z)
& greater(X,Y) )
=> greater(X,Z) ),
file('theBenchmark.p',mp_greater_transitivity) ).
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(l8,axiom,
! [E,T] :
( ( greater(T,critical_point(E))
& in_environment(E,T)
& environment(E) )
=> selection_favors(efficient_producers,first_movers,T) ),
file('theBenchmark.p',l8) ).
fof(prove_t8,conjecture,
! [P] :
( ( slow_change(P)
& observational_period(P) )
=> selection_favors(efficient_producers,first_movers,P) ),
file('theBenchmark.p',prove_t8) ).
fof(prove_t8_neg,negated_conjecture,
~ ! [P] :
( ( slow_change(P)
& observational_period(P) )
=> selection_favors(efficient_producers,first_movers,P) ),
inference(assume_negation,[status(cth)],[prove_t8]) ).
fof(nnf_10,plain,
? [P] :
( ~ selection_favors(efficient_producers,first_movers,P)
& slow_change(P)
& observational_period(P) ),
inference(fof_nnf,[status(thm)],[prove_t8_neg]) ).
fof(sk_prove_t8_neg,plain,
( ~ selection_favors(efficient_producers,first_movers,sK0)
& slow_change(sK0)
& observational_period(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(P,sK0)],[nnf_10]) ).
cnf(c_11,negated_conjecture,
observational_period(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_t8_neg]) ).
fof(nnf_2,plain,
! [P] :
( ! [E] :
( ? [T] :
( greater(T,critical_point(E))
& in_environment(E,T) )
| ~ in_environment(P,E)
| ~ environment(E) )
| ~ slow_change(P)
| ~ observational_period(P) ),
inference(fof_nnf,[status(thm)],[mp4_critical_point]) ).
fof(sk_mp4_critical_point_sk,plain,
! [P] :
( ! [E] :
( ( greater(sK1(P,E),critical_point(E))
& in_environment(E,sK1(P,E)) )
| ~ in_environment(P,E)
| ~ environment(E) )
| ~ slow_change(P)
| ~ observational_period(P) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(T,sK1(P,E))],[nnf_2]) ).
fof(sk_mp4_critical_point,plain,
( ! [VAR_0,VAR_1] :
( greater(sK1(VAR_0,VAR_1),critical_point(VAR_1))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_1)
| ~ slow_change(VAR_0)
| ~ observational_period(VAR_0) )
& ! [VAR_0,VAR_1] :
( in_environment(VAR_1,sK1(VAR_0,VAR_1))
| ~ in_environment(VAR_0,VAR_1)
| ~ environment(VAR_1)
| ~ slow_change(VAR_0)
| ~ observational_period(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_mp4_critical_point_sk]) ).
cnf(c_12,plain,
( greater(sK1(A,B),critical_point(B))
| ~ in_environment(A,B)
| ~ environment(B)
| ~ slow_change(A)
| ~ observational_period(A) ),
inference(split_conjunct,[status(thm)],[sk_mp4_critical_point]) ).
cnf(c_13,plain,
( in_environment(B,sK1(A,B))
| ~ in_environment(A,B)
| ~ environment(B)
| ~ slow_change(A)
| ~ observational_period(A) ),
inference(split_conjunct,[status(thm)],[sk_mp4_critical_point]) ).
fof(nnf_1,plain,
! [P] :
( selection_favors(efficient_producers,first_movers,P)
| ? [E] :
( ~ selection_favors(efficient_producers,first_movers,end_time(E))
& in_environment(P,E)
& environment(E) )
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(P) ),
inference(fof_nnf,[status(thm)],[mp3_favoured_trategy]) ).
fof(sk_mp3_favoured_trategy_sk,plain,
! [P] :
( selection_favors(efficient_producers,first_movers,P)
| ( ~ selection_favors(efficient_producers,first_movers,end_time(sK2(P)))
& in_environment(P,sK2(P))
& environment(sK2(P)) )
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(P) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(E,sK2(P))],[nnf_1]) ).
fof(sk_mp3_favoured_trategy,plain,
( ! [VAR_0] :
( selection_favors(efficient_producers,first_movers,VAR_0)
| ~ selection_favors(efficient_producers,first_movers,end_time(sK2(VAR_0)))
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(VAR_0) )
& ! [VAR_0] :
( selection_favors(efficient_producers,first_movers,VAR_0)
| in_environment(VAR_0,sK2(VAR_0))
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(VAR_0) )
& ! [VAR_0] :
( selection_favors(efficient_producers,first_movers,VAR_0)
| environment(sK2(VAR_0))
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_mp3_favoured_trategy_sk]) ).
cnf(c_14,plain,
( selection_favors(efficient_producers,first_movers,A)
| ~ selection_favors(efficient_producers,first_movers,end_time(sK2(A)))
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(A) ),
inference(split_conjunct,[status(thm)],[sk_mp3_favoured_trategy]) ).
cnf(c_15,plain,
( selection_favors(efficient_producers,first_movers,A)
| in_environment(A,sK2(A))
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(A) ),
inference(split_conjunct,[status(thm)],[sk_mp3_favoured_trategy]) ).
cnf(c_16,plain,
( selection_favors(efficient_producers,first_movers,A)
| environment(sK2(A))
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| ~ observational_period(A) ),
inference(split_conjunct,[status(thm)],[sk_mp3_favoured_trategy]) ).
cnf(c_17,negated_conjecture,
( in_environment(A,sK1(sK0,A))
| ~ in_environment(sK0,A)
| ~ environment(A)
| ~ slow_change(sK0) ),
inference(resolve,[status(thm)],[c_11,c_13]) ).
cnf(c_18,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| environment(sK2(sK0))
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers) ),
inference(resolve,[status(thm)],[c_11,c_16]) ).
cnf(c_19,negated_conjecture,
( greater(sK1(sK0,A),critical_point(A))
| ~ in_environment(sK0,A)
| ~ environment(A)
| ~ slow_change(sK0) ),
inference(resolve,[status(thm)],[c_11,c_12]) ).
cnf(c_20,plain,
( selection_favors(efficient_producers,first_movers,B)
| ~ greater(B,critical_point(A))
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[l8]) ).
cnf(c_22,plain,
( greater_or_equal(critical_point(A),start_time(A))
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_time_of_critical_point]) ).
cnf(c_23,plain,
( greater_or_equal(end_time(A),B)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(clausify,[status(thm)],[mp_environment_end_point]) ).
cnf(c_24,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]) ).
cnf(c_25,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| in_environment(sK2(sK0),A)
| ~ greater_or_equal(end_time(sK2(sK0)),A)
| ~ greater_or_equal(A,start_time(sK2(sK0))) ),
inference(resolve,[status(thm)],[c_24,c_18]) ).
cnf(c_26,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| greater_or_equal(end_time(sK2(sK0)),A)
| ~ in_environment(sK2(sK0),A) ),
inference(resolve,[status(thm)],[c_23,c_18]) ).
cnf(c_27,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| greater_or_equal(critical_point(sK2(sK0)),start_time(sK2(sK0))) ),
inference(resolve,[status(thm)],[c_22,c_18]) ).
cnf(c_29,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| selection_favors(efficient_producers,first_movers,A)
| ~ greater(A,critical_point(sK2(sK0)))
| ~ in_environment(sK2(sK0),A) ),
inference(resolve,[status(thm)],[c_20,c_18]) ).
cnf(c_30,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| greater(sK1(sK0,sK2(sK0)),critical_point(sK2(sK0)))
| ~ in_environment(sK0,sK2(sK0))
| ~ slow_change(sK0) ),
inference(resolve,[status(thm)],[c_19,c_18]) ).
cnf(c_31,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| in_environment(sK2(sK0),sK1(sK0,sK2(sK0)))
| ~ in_environment(sK0,sK2(sK0))
| ~ slow_change(sK0) ),
inference(resolve,[status(thm)],[c_17,c_18]) ).
fof(mp_organizational_sets1,axiom,
propagation_strategy(first_movers),
file('theBenchmark.p',mp_organizational_sets1) ).
cnf(c_32,plain,
propagation_strategy(first_movers),
inference(clausify,[status(thm)],[mp_organizational_sets1]) ).
fof(mp_organizational_sets2,axiom,
propagation_strategy(efficient_producers),
file('theBenchmark.p',mp_organizational_sets2) ).
cnf(c_33,plain,
propagation_strategy(efficient_producers),
inference(clausify,[status(thm)],[mp_organizational_sets2]) ).
cnf(c_34,plain,
( greater(A,C)
| ~ greater(B,C)
| ~ greater(A,B) ),
inference(clausify,[status(thm)],[mp_greater_transitivity]) ).
cnf(c_35,plain,
( B = A
| greater(A,B)
| ~ greater_or_equal(A,B) ),
inference(clausify,[status(thm)],[mp_greater_or_equal]) ).
cnf(c_36,plain,
( ~ greater(A,B)
| greater_or_equal(A,B) ),
inference(clausify,[status(thm)],[mp_greater_or_equal]) ).
cnf(c_37,plain,
( B != A
| greater_or_equal(A,B) ),
inference(clausify,[status(thm)],[mp_greater_or_equal]) ).
cnf(c_38,negated_conjecture,
slow_change(sK0),
inference(split_conjunct,[status(thm)],[sk_prove_t8_neg]) ).
cnf(c_39,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,sK0),
inference(split_conjunct,[status(thm)],[sk_prove_t8_neg]) ).
cnf(c_40,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| ~ selection_favors(efficient_producers,first_movers,end_time(sK2(sK0)))
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers) ),
inference(resolve,[status(thm)],[c_11,c_14]) ).
cnf(c_110,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| ~ selection_favors(efficient_producers,first_movers,end_time(sK2(sK0)))
| ~ propagation_strategy(efficient_producers) ),
inference(resolve,[status(thm)],[c_32,c_40]) ).
cnf(c_111,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| ~ selection_favors(efficient_producers,first_movers,end_time(sK2(sK0))) ),
inference(resolve,[status(thm)],[c_33,c_110]) ).
cnf(c_41,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,end_time(sK2(sK0))),
inference(resolve,[status(thm)],[c_39,c_111]) ).
cnf(c_42,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| in_environment(sK0,sK2(sK0))
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers) ),
inference(resolve,[status(thm)],[c_11,c_15]) ).
cnf(c_112,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| in_environment(sK0,sK2(sK0))
| ~ propagation_strategy(efficient_producers) ),
inference(resolve,[status(thm)],[c_32,c_42]) ).
cnf(c_113,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| in_environment(sK0,sK2(sK0)) ),
inference(resolve,[status(thm)],[c_33,c_112]) ).
cnf(c_43,negated_conjecture,
in_environment(sK0,sK2(sK0)),
inference(resolve,[status(thm)],[c_39,c_113]) ).
cnf(c_114,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| in_environment(sK2(sK0),sK1(sK0,sK2(sK0)))
| ~ in_environment(sK0,sK2(sK0)) ),
inference(resolve,[status(thm)],[c_38,c_31]) ).
cnf(c_115,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| in_environment(sK2(sK0),sK1(sK0,sK2(sK0))) ),
inference(resolve,[status(thm)],[c_43,c_114]) ).
cnf(c_116,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| ~ propagation_strategy(efficient_producers)
| in_environment(sK2(sK0),sK1(sK0,sK2(sK0))) ),
inference(resolve,[status(thm)],[c_32,c_115]) ).
cnf(c_117,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| in_environment(sK2(sK0),sK1(sK0,sK2(sK0))) ),
inference(resolve,[status(thm)],[c_33,c_116]) ).
cnf(c_45,negated_conjecture,
in_environment(sK2(sK0),sK1(sK0,sK2(sK0))),
inference(resolve,[status(thm)],[c_39,c_117]) ).
cnf(c_118,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| greater(sK1(sK0,sK2(sK0)),critical_point(sK2(sK0)))
| ~ in_environment(sK0,sK2(sK0)) ),
inference(resolve,[status(thm)],[c_38,c_30]) ).
cnf(c_119,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| ~ propagation_strategy(efficient_producers)
| ~ propagation_strategy(first_movers)
| greater(sK1(sK0,sK2(sK0)),critical_point(sK2(sK0))) ),
inference(resolve,[status(thm)],[c_43,c_118]) ).
cnf(c_120,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| ~ propagation_strategy(efficient_producers)
| greater(sK1(sK0,sK2(sK0)),critical_point(sK2(sK0))) ),
inference(resolve,[status(thm)],[c_32,c_119]) ).
cnf(c_121,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| greater(sK1(sK0,sK2(sK0)),critical_point(sK2(sK0))) ),
inference(resolve,[status(thm)],[c_33,c_120]) ).
cnf(c_46,negated_conjecture,
greater(sK1(sK0,sK2(sK0)),critical_point(sK2(sK0))),
inference(resolve,[status(thm)],[c_39,c_121]) ).
cnf(c_122,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| ~ propagation_strategy(efficient_producers)
| selection_favors(efficient_producers,first_movers,A)
| ~ greater(A,critical_point(sK2(sK0)))
| ~ in_environment(sK2(sK0),A) ),
inference(resolve,[status(thm)],[c_32,c_29]) ).
cnf(c_123,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| selection_favors(efficient_producers,first_movers,A)
| ~ greater(A,critical_point(sK2(sK0)))
| ~ in_environment(sK2(sK0),A) ),
inference(resolve,[status(thm)],[c_33,c_122]) ).
cnf(c_47,negated_conjecture,
( selection_favors(efficient_producers,first_movers,A)
| ~ greater(A,critical_point(sK2(sK0)))
| ~ in_environment(sK2(sK0),A) ),
inference(resolve,[status(thm)],[c_39,c_123]) ).
cnf(c_124,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| ~ propagation_strategy(efficient_producers)
| greater_or_equal(critical_point(sK2(sK0)),start_time(sK2(sK0))) ),
inference(resolve,[status(thm)],[c_32,c_27]) ).
cnf(c_125,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| greater_or_equal(critical_point(sK2(sK0)),start_time(sK2(sK0))) ),
inference(resolve,[status(thm)],[c_33,c_124]) ).
cnf(c_49,negated_conjecture,
greater_or_equal(critical_point(sK2(sK0)),start_time(sK2(sK0))),
inference(resolve,[status(thm)],[c_39,c_125]) ).
cnf(c_126,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| ~ propagation_strategy(efficient_producers)
| greater_or_equal(end_time(sK2(sK0)),A)
| ~ in_environment(sK2(sK0),A) ),
inference(resolve,[status(thm)],[c_32,c_26]) ).
cnf(c_127,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| greater_or_equal(end_time(sK2(sK0)),A)
| ~ in_environment(sK2(sK0),A) ),
inference(resolve,[status(thm)],[c_33,c_126]) ).
cnf(c_50,negated_conjecture,
( greater_or_equal(end_time(sK2(sK0)),A)
| ~ in_environment(sK2(sK0),A) ),
inference(resolve,[status(thm)],[c_39,c_127]) ).
cnf(c_128,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| ~ propagation_strategy(efficient_producers)
| in_environment(sK2(sK0),A)
| ~ greater_or_equal(end_time(sK2(sK0)),A)
| ~ greater_or_equal(A,start_time(sK2(sK0))) ),
inference(resolve,[status(thm)],[c_32,c_25]) ).
cnf(c_129,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK0)
| in_environment(sK2(sK0),A)
| ~ greater_or_equal(end_time(sK2(sK0)),A)
| ~ greater_or_equal(A,start_time(sK2(sK0))) ),
inference(resolve,[status(thm)],[c_33,c_128]) ).
cnf(c_51,negated_conjecture,
( in_environment(sK2(sK0),A)
| ~ greater_or_equal(end_time(sK2(sK0)),A)
| ~ greater_or_equal(A,start_time(sK2(sK0))) ),
inference(resolve,[status(thm)],[c_39,c_129]) ).
cnf(c_52,plain,
greater_or_equal(A,A),
inference(xxres,[status(thm)],[c_37]) ).
cnf(c_54,plain,
( greater(A,critical_point(sK2(sK0)))
| ~ greater(A,sK1(sK0,sK2(sK0))) ),
inference(resolve,[status(thm)],[c_46,c_34]) ).
cnf(c_130,negated_conjecture,
( selection_favors(efficient_producers,first_movers,sK1(sK0,sK2(sK0)))
| ~ greater(sK1(sK0,sK2(sK0)),critical_point(sK2(sK0))) ),
inference(resolve,[status(thm)],[c_47,c_45]) ).
cnf(c_56,negated_conjecture,
selection_favors(efficient_producers,first_movers,sK1(sK0,sK2(sK0))),
inference(resolve,[status(thm)],[c_46,c_130]) ).
cnf(c_57,plain,
( start_time(sK2(sK0)) = critical_point(sK2(sK0))
| greater(critical_point(sK2(sK0)),start_time(sK2(sK0))) ),
inference(resolve,[status(thm)],[c_49,c_35]) ).
cnf(c_58,plain,
greater_or_equal(end_time(sK2(sK0)),sK1(sK0,sK2(sK0))),
inference(resolve,[status(thm)],[c_50,c_45]) ).
cnf(c_60,plain,
( in_environment(sK2(sK0),end_time(sK2(sK0)))
| ~ greater_or_equal(end_time(sK2(sK0)),start_time(sK2(sK0))) ),
inference(resolve,[status(thm)],[c_52,c_51]) ).
cnf(c_131,plain,
( sK1(sK0,sK2(sK0)) = end_time(sK2(sK0))
| greater(end_time(sK2(sK0)),sK1(sK0,sK2(sK0))) ),
inference(resolve,[status(thm)],[c_58,c_35]) ).
cnf(c_62,plain,
( end_time(sK2(sK0)) = sK1(sK0,sK2(sK0))
| greater(end_time(sK2(sK0)),sK1(sK0,sK2(sK0))) ),
inference(copy,[status(thm)],[c_131]) ).
cnf(c_65,plain,
( greater(A,start_time(sK2(sK0)))
| ~ greater(A,critical_point(sK2(sK0)))
| start_time(sK2(sK0)) = critical_point(sK2(sK0)) ),
inference(resolve,[status(thm)],[c_57,c_34]) ).
cnf(c_67,plain,
( greater(end_time(sK2(sK0)),critical_point(sK2(sK0)))
| end_time(sK2(sK0)) = sK1(sK0,sK2(sK0)) ),
inference(resolve,[status(thm)],[c_62,c_54]) ).
cnf(c_73,plain,
( greater_or_equal(end_time(sK2(sK0)),critical_point(sK2(sK0)))
| end_time(sK2(sK0)) = sK1(sK0,sK2(sK0)) ),
inference(resolve,[status(thm)],[c_67,c_36]) ).
cnf(c_80,plain,
( end_time(sK2(sK0)) = sK1(sK0,sK2(sK0))
| greater(end_time(sK2(sK0)),start_time(sK2(sK0)))
| start_time(sK2(sK0)) = critical_point(sK2(sK0)) ),
inference(resolve,[status(thm)],[c_65,c_67]) ).
cnf(c_82,plain,
( greater_or_equal(end_time(sK2(sK0)),start_time(sK2(sK0)))
| end_time(sK2(sK0)) = sK1(sK0,sK2(sK0))
| start_time(sK2(sK0)) = critical_point(sK2(sK0)) ),
inference(resolve,[status(thm)],[c_80,c_36]) ).
cnf(c_86,plain,
( in_environment(sK2(sK0),end_time(sK2(sK0)))
| end_time(sK2(sK0)) = sK1(sK0,sK2(sK0))
| start_time(sK2(sK0)) = critical_point(sK2(sK0)) ),
inference(resolve,[status(thm)],[c_82,c_60]) ).
cnf(c_132,negated_conjecture,
( selection_favors(efficient_producers,first_movers,end_time(sK2(sK0)))
| ~ greater(end_time(sK2(sK0)),critical_point(sK2(sK0)))
| end_time(sK2(sK0)) = sK1(sK0,sK2(sK0))
| start_time(sK2(sK0)) = critical_point(sK2(sK0)) ),
inference(resolve,[status(thm)],[c_86,c_47]) ).
cnf(c_92,negated_conjecture,
( ~ greater(end_time(sK2(sK0)),critical_point(sK2(sK0)))
| end_time(sK2(sK0)) = sK1(sK0,sK2(sK0))
| start_time(sK2(sK0)) = critical_point(sK2(sK0)) ),
inference(resolve,[status(thm)],[c_41,c_132]) ).
cnf(c_133,plain,
( end_time(sK2(sK0)) = sK1(sK0,sK2(sK0))
| end_time(sK2(sK0)) = sK1(sK0,sK2(sK0))
| start_time(sK2(sK0)) = critical_point(sK2(sK0)) ),
inference(resolve,[status(thm)],[c_92,c_67]) ).
cnf(c_93,plain,
( end_time(sK2(sK0)) = sK1(sK0,sK2(sK0))
| start_time(sK2(sK0)) = critical_point(sK2(sK0)) ),
inference(copy,[status(thm)],[c_133]) ).
cnf(c_97,plain,
( in_environment(sK2(sK0),end_time(sK2(sK0)))
| ~ greater_or_equal(end_time(sK2(sK0)),critical_point(sK2(sK0)))
| end_time(sK2(sK0)) = sK1(sK0,sK2(sK0)) ),
inference(paramod,[status(thm)],[c_93,c_60]) ).
cnf(c_134,plain,
( end_time(sK2(sK0)) = sK1(sK0,sK2(sK0))
| in_environment(sK2(sK0),end_time(sK2(sK0)))
| end_time(sK2(sK0)) = sK1(sK0,sK2(sK0)) ),
inference(resolve,[status(thm)],[c_97,c_73]) ).
cnf(c_99,plain,
( in_environment(sK2(sK0),end_time(sK2(sK0)))
| end_time(sK2(sK0)) = sK1(sK0,sK2(sK0)) ),
inference(copy,[status(thm)],[c_134]) ).
cnf(c_135,negated_conjecture,
( selection_favors(efficient_producers,first_movers,end_time(sK2(sK0)))
| ~ greater(end_time(sK2(sK0)),critical_point(sK2(sK0)))
| end_time(sK2(sK0)) = sK1(sK0,sK2(sK0)) ),
inference(resolve,[status(thm)],[c_99,c_47]) ).
cnf(c_100,negated_conjecture,
( ~ greater(end_time(sK2(sK0)),critical_point(sK2(sK0)))
| end_time(sK2(sK0)) = sK1(sK0,sK2(sK0)) ),
inference(resolve,[status(thm)],[c_41,c_135]) ).
cnf(c_136,plain,
( end_time(sK2(sK0)) = sK1(sK0,sK2(sK0))
| end_time(sK2(sK0)) = sK1(sK0,sK2(sK0)) ),
inference(resolve,[status(thm)],[c_100,c_67]) ).
cnf(c_101,plain,
end_time(sK2(sK0)) = sK1(sK0,sK2(sK0)),
inference(copy,[status(thm)],[c_136]) ).
cnf(c_137,negated_conjecture,
~ selection_favors(efficient_producers,first_movers,sK1(sK0,sK2(sK0))),
inference(paramod,[status(thm)],[c_101,c_41]) ).
cnf(c_109,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_56,c_137]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT039+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 00:07:04 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 4048406 was started by sandbox2 on n019,
% 0.08/0.36 % Sat Sep 26 00:07:04 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.13/0.38
% 0.13/0.38 % SZS status Theorem for theBenchmark
% 0.13/0.38
% 0.13/0.38 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.13/0.38 % Length of proof is 66.
% 0.13/0.38 % Level of proof is 17.
% 0.13/0.38 % Maximum clause weight is 22.000.
% 0.13/0.38 % Given clauses 57.
% 0.13/0.38
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------