%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT020+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 : Fri Sep 25 02:11:19 PM UTC 2026
% Result : Theorem 4.50s 1.05s
% Output : Proof 4.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 67 ( 11 unt; 0 def)
% Number of atoms : 201 ( 18 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 223 ( 89 ~; 103 |; 18 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 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 : 85 ( 0 sgn 55 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_times_in_order) ).
fof(f5_nnf,plain,
! [E,T1,T2] :
( in_environment(E,T1)
| ~ in_environment(E,T2)
| ~ greater(T2,T1)
| ~ greater_or_equal(T1,start_time(E))
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [E,T1,T2] :
( in_environment(E,T1)
| ~ in_environment(E,T2)
| ~ greater(T2,T1)
| ~ greater_or_equal(T1,start_time(E))
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c6,plain,
( in_environment(X0,X1)
| ~ in_environment(X0,X2)
| ~ greater(X2,X1)
| ~ greater_or_equal(X1,start_time(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f10,conjecture,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> greater(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l2) ).
fof(f10_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(negated_conjecture,[status(cth)],[f10]) ).
fof(f10_nnf,plain,
? [E,T] :
( ~ greater(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))
& subpopulations(first_movers,efficient_producers,E,T)
& environment(E) ),
inference(nnf_transformation,[status(thm)],[f10_neg]) ).
fof(f10_sk,plain,
( ~ greater(disbanding_rate(first_movers,sk1),disbanding_rate(efficient_producers,sk1))
& subpopulations(first_movers,efficient_producers,sk0,sk1)
& environment(sk0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk0,sk1])],[f10_nnf]) ).
cnf(c11,plain,
environment(sk0),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p35,plain,
( in_environment(sk0,X0)
| ~ in_environment(sk0,X1)
| ~ greater(X1,X0)
| ~ greater_or_equal(X0,start_time(sk0)) ),
inference(resolution,[status(thm)],[c6,c11]) ).
fof(f4,axiom,
! [E] :
( environment(E)
=> greater_or_equal(initial_FM_EP(E),start_time(E)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_initial_time) ).
fof(f4_nnf,plain,
! [E] :
( greater_or_equal(initial_FM_EP(E),start_time(E))
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [E] :
( greater_or_equal(initial_FM_EP(E),start_time(E))
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c5,plain,
( greater_or_equal(initial_FM_EP(X0),start_time(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p14,plain,
greater_or_equal(initial_FM_EP(sk0),start_time(sk0)),
inference(resolution,[status(thm)],[c5,c11]) ).
cnf(p36,plain,
( in_environment(sk0,initial_FM_EP(sk0))
| ~ in_environment(sk0,X0)
| ~ greater(X0,initial_FM_EP(sk0)) ),
inference(resolution,[status(thm)],[p35,p14]) ).
fof(f1,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_point) ).
fof(f1_nnf,plain,
! [E,T] :
( ( ( greater_or_equal(T,initial_FM_EP(E))
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ( subpopulations(first_movers,efficient_producers,E,initial_FM_EP(E))
| ~ in_environment(E,initial_FM_EP(E)) ) )
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [E,T] :
( ( ( greater_or_equal(T,initial_FM_EP(E))
| ~ subpopulations(first_movers,efficient_producers,E,T) )
& ( subpopulations(first_movers,efficient_producers,E,initial_FM_EP(E))
| ~ in_environment(E,initial_FM_EP(E)) ) )
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c2,plain,
( greater_or_equal(X1,initial_FM_EP(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p20,plain,
( greater_or_equal(X0,initial_FM_EP(sk0))
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[c2,c11]) ).
cnf(c12,plain,
subpopulations(first_movers,efficient_producers,sk0,sk1),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p21,plain,
greater_or_equal(sk1,initial_FM_EP(sk0)),
inference(resolution,[status(thm)],[p20,c12]) ).
fof(f7,axiom,
! [X,Y] :
( greater_or_equal(X,Y)
=> ( X = Y
| greater(X,Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(f7_nnf,plain,
! [X,Y] :
( X = Y
| greater(X,Y)
| ~ greater_or_equal(X,Y) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] :
( X = Y
| greater(X,Y)
| ~ greater_or_equal(X,Y) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c8,plain,
( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p22,plain,
( sk1 = initial_FM_EP(sk0)
| greater(sk1,initial_FM_EP(sk0)) ),
inference(resolution,[status(thm)],[p21,c8]) ).
cnf(p38,plain,
( sk1 = initial_FM_EP(sk0)
| in_environment(sk0,initial_FM_EP(sk0))
| ~ in_environment(sk0,sk1) ),
inference(resolution,[status(thm)],[p36,p22]) ).
fof(f3,axiom,
! [E,T] :
( ( subpopulations(first_movers,efficient_producers,E,T)
& environment(E) )
=> in_environment(E,T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occurs) ).
fof(f3_nnf,plain,
! [E,T] :
( in_environment(E,T)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [E,T] :
( in_environment(E,T)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c4,plain,
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p30,plain,
( in_environment(sk0,X0)
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[c4,c11]) ).
cnf(p31,plain,
in_environment(sk0,sk1),
inference(resolution,[status(thm)],[p30,c12]) ).
cnf(p39,plain,
( sk1 = initial_FM_EP(sk0)
| in_environment(sk0,initial_FM_EP(sk0)) ),
inference(resolution,[status(thm)],[p38,p31]) ).
cnf(c1,plain,
( subpopulations(first_movers,efficient_producers,X0,initial_FM_EP(X0))
| ~ in_environment(X0,initial_FM_EP(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p17,plain,
( subpopulations(first_movers,efficient_producers,sk0,initial_FM_EP(sk0))
| ~ in_environment(sk0,initial_FM_EP(sk0)) ),
inference(resolution,[status(thm)],[c1,c11]) ).
cnf(p40,plain,
( subpopulations(first_movers,efficient_producers,sk0,initial_FM_EP(sk0))
| sk1 = initial_FM_EP(sk0) ),
inference(resolution,[status(thm)],[p39,p17]) ).
cnf(p44,plain,
( greater_or_equal(initial_FM_EP(sk0),initial_FM_EP(sk0))
| sk1 = initial_FM_EP(sk0) ),
inference(resolution,[status(thm)],[p40,p20]) ).
fof(f2,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_positive_function_difference) ).
fof(f2_nnf,plain,
! [E,T,T1,T2] :
( greater(disbanding_rate(first_movers,T2),disbanding_rate(efficient_producers,T2))
| decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
| ~ 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) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [E,T,T1,T2] :
( greater(disbanding_rate(first_movers,T2),disbanding_rate(efficient_producers,T2))
| decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
| ~ 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) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c3,plain,
( greater(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3))
| decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater_or_equal(X3,X1)
| ~ greater_or_equal(X1,X2)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p25,plain,
( greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))
| decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ greater(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))
| ~ subpopulations(first_movers,efficient_producers,sk0,X2)
| ~ greater_or_equal(X2,X0)
| ~ greater_or_equal(X0,X1) ),
inference(resolution,[status(thm)],[c3,c11]) ).
cnf(p45,plain,
( greater(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))
| 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)))
| ~ subpopulations(first_movers,efficient_producers,sk0,X0)
| ~ greater_or_equal(X0,initial_FM_EP(sk0))
| sk1 = initial_FM_EP(sk0) ),
inference(resolution,[status(thm)],[p44,p25]) ).
cnf(p58,plain,
( greater(disbanding_rate(first_movers,sk1),disbanding_rate(efficient_producers,sk1))
| 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)))
| ~ subpopulations(first_movers,efficient_producers,sk0,sk1)
| sk1 = initial_FM_EP(sk0) ),
inference(resolution,[status(thm)],[p45,p21]) ).
cnf(p59,plain,
( greater(disbanding_rate(first_movers,sk1),disbanding_rate(efficient_producers,sk1))
| 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)))
| sk1 = initial_FM_EP(sk0) ),
inference(resolution,[status(thm)],[p58,c12]) ).
fof(f8,hypothesis,
! [E] :
( environment(E)
=> greater(disbanding_rate(first_movers,initial_FM_EP(E)),disbanding_rate(efficient_producers,initial_FM_EP(E))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a8) ).
fof(f8_nnf,plain,
! [E] :
( greater(disbanding_rate(first_movers,initial_FM_EP(E)),disbanding_rate(efficient_producers,initial_FM_EP(E)))
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [E] :
( greater(disbanding_rate(first_movers,initial_FM_EP(E)),disbanding_rate(efficient_producers,initial_FM_EP(E)))
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c9,plain,
( greater(disbanding_rate(first_movers,initial_FM_EP(X0)),disbanding_rate(efficient_producers,initial_FM_EP(X0)))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p41,plain,
greater(disbanding_rate(first_movers,initial_FM_EP(sk0)),disbanding_rate(efficient_producers,initial_FM_EP(sk0))),
inference(resolution,[status(thm)],[c9,c11]) ).
cnf(p60,plain,
( greater(disbanding_rate(first_movers,sk1),disbanding_rate(efficient_producers,sk1))
| decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sk0)),disbanding_rate(efficient_producers,initial_FM_EP(sk0))))
| sk1 = initial_FM_EP(sk0) ),
inference(resolution,[status(thm)],[p59,p41]) ).
fof(f0,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('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3) ).
fof(f0_nnf,plain,
! [E,T] :
( ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [E,T] :
( ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
| ~ subpopulations(first_movers,efficient_producers,E,T)
| ~ environment(E) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p15,plain,
( ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sk0,X0) ),
inference(resolution,[status(thm)],[c0,c11]) ).
cnf(p43,plain,
( ~ decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sk0)),disbanding_rate(efficient_producers,initial_FM_EP(sk0))))
| sk1 = initial_FM_EP(sk0) ),
inference(resolution,[status(thm)],[p40,p15]) ).
cnf(p61,plain,
( sk1 = initial_FM_EP(sk0)
| greater(disbanding_rate(first_movers,sk1),disbanding_rate(efficient_producers,sk1))
| sk1 = initial_FM_EP(sk0) ),
inference(resolution,[status(thm)],[p60,p43]) ).
cnf(p62,plain,
( greater(disbanding_rate(first_movers,sk1),disbanding_rate(efficient_producers,sk1))
| sk1 = initial_FM_EP(sk0) ),
inference(factoring,[status(thm)],[p61]) ).
cnf(c13,plain,
~ greater(disbanding_rate(first_movers,sk1),disbanding_rate(efficient_producers,sk1)),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p63,plain,
sk1 = initial_FM_EP(sk0),
inference(resolution,[status(thm)],[p62,c13]) ).
cnf(p70,plain,
greater(disbanding_rate(first_movers,sk1),disbanding_rate(efficient_producers,initial_FM_EP(sk0))),
inference(superposition,[status(thm)],[p63,p41]) ).
cnf(p77,plain,
greater(disbanding_rate(first_movers,sk1),disbanding_rate(efficient_producers,sk1)),
inference(superposition,[status(thm)],[p63,p70]) ).
cnf(p89,plain,
$false,
inference(resolution,[status(thm)],[p77,c13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT020+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.38 % Computer : n017.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 00:57:00 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.50/1.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.50/1.05 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------