%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT020+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 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 : Fri Sep 25 02:12:22 PM UTC 2026
% Result : Theorem 2.29s 11.30s
% Output : CNFRefutation 2.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 16
% Syntax : Number of formulae : 121 ( 25 unt; 6 def)
% Number of atoms : 461 ( 30 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 455 ( 208 ~; 210 |; 23 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 7 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 164 ( 0 sgn 160 !; 4 ?; 75 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3) ).
fof(f2,axiom,
! [X0,X1] :
( environment(X0)
=> ( ( subpopulations(first_movers,efficient_producers,X0,X1)
=> greater_or_equal(X1,initial_FM_EP(X0)) )
& ( in_environment(X0,initial_FM_EP(X0))
=> subpopulations(first_movers,efficient_producers,X0,initial_FM_EP(X0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_earliest_time_point) ).
fof(f3,axiom,
! [X0,X1,X2,X3] :
( ( 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) )
=> ( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
=> greater(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_positive_function_difference) ).
fof(f4,axiom,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> in_environment(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occurs) ).
fof(f5,axiom,
! [X0] :
( environment(X0)
=> greater_or_equal(initial_FM_EP(X0),start_time(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_initial_time) ).
fof(f6,axiom,
! [X0,X1,X2] :
( ( in_environment(X0,X2)
& greater(X2,X1)
& greater_or_equal(X1,start_time(X0))
& environment(X0) )
=> in_environment(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_times_in_order) ).
fof(f8,axiom,
! [X0,X1] :
( greater_or_equal(X0,X1)
=> ( X0 = X1
| greater(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(f9,axiom,
! [X0] :
( environment(X0)
=> greater(disbanding_rate(first_movers,initial_FM_EP(X0)),disbanding_rate(efficient_producers,initial_FM_EP(X0))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a8) ).
fof(f10,axiom,
! [X0,X1,X2,X3] :
( ( greater_or_equal(X2,X3)
& greater_or_equal(X3,X1)
& subpopulations(first_movers,efficient_producers,X0,X2)
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> subpopulations(first_movers,efficient_producers,X0,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a10) ).
fof(f11,conjecture,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> greater(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l2) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> greater(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(ennf_transformation,[],[f1]) ).
fof(f14,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ~ environment(X0)
| ( ( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater_or_equal(X1,initial_FM_EP(X0)) )
& ( ~ in_environment(X0,initial_FM_EP(X0))
| subpopulations(first_movers,efficient_producers,X0,initial_FM_EP(X0)) ) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( ~ 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)
| decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| greater(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3)) ),
inference(ennf_transformation,[],[f3]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( ~ 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)
| decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| greater(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3)) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(ennf_transformation,[],[f4]) ).
fof(f19,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0] :
( ~ environment(X0)
| greater_or_equal(initial_FM_EP(X0),start_time(X0)) ),
inference(ennf_transformation,[],[f5]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ~ in_environment(X0,X2)
| ~ greater(X2,X1)
| ~ greater_or_equal(X1,start_time(X0))
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f22,plain,
! [X0,X1,X2] :
( ~ in_environment(X0,X2)
| ~ greater(X2,X1)
| ~ greater_or_equal(X1,start_time(X0))
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(flattening,[],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| X0 = X1
| greater(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f26,plain,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| X0 = X1
| greater(X0,X1) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0] :
( ~ environment(X0)
| greater(disbanding_rate(first_movers,initial_FM_EP(X0)),disbanding_rate(efficient_producers,initial_FM_EP(X0))) ),
inference(ennf_transformation,[],[f9]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ~ greater_or_equal(X2,X3)
| ~ greater_or_equal(X3,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,X3) ),
inference(ennf_transformation,[],[f10]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( ~ greater_or_equal(X2,X3)
| ~ greater_or_equal(X3,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,X3) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
? [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0)
& ~ greater(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)) ),
inference(ennf_transformation,[],[f12]) ).
fof(f31,plain,
? [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0)
& ~ greater(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
( subpopulations(first_movers,efficient_producers,sK0,sK1)
& environment(sK0)
& ~ greater(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(cnf_transformation,[],[f14]) ).
fof(f34,plain,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater_or_equal(X1,initial_FM_EP(X0)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f35,plain,
! [X0] :
( ~ environment(X0)
| ~ in_environment(X0,initial_FM_EP(X0))
| subpopulations(first_movers,efficient_producers,X0,initial_FM_EP(X0)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f36,plain,
! [X2,X3,X0,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)
| decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| greater(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3)) ),
inference(cnf_transformation,[],[f17]) ).
fof(f37,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f38,plain,
! [X0] :
( ~ environment(X0)
| greater_or_equal(initial_FM_EP(X0),start_time(X0)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X2,X0,X1] :
( ~ in_environment(X0,X2)
| ~ greater(X2,X1)
| ~ greater_or_equal(X1,start_time(X0))
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
fof(f41,plain,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| X0 = X1
| greater(X0,X1) ),
inference(cnf_transformation,[],[f26]) ).
fof(f42,plain,
! [X0] :
( ~ environment(X0)
| greater(disbanding_rate(first_movers,initial_FM_EP(X0)),disbanding_rate(efficient_producers,initial_FM_EP(X0))) ),
inference(cnf_transformation,[],[f27]) ).
fof(f43,plain,
! [X2,X3,X0,X1] :
( ~ greater_or_equal(X2,X3)
| ~ greater_or_equal(X3,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,X3) ),
inference(cnf_transformation,[],[f29]) ).
fof(f44,plain,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f32]) ).
fof(f45,plain,
environment(sK0),
inference(cnf_transformation,[],[f32]) ).
fof(f46,plain,
~ greater(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)),
inference(cnf_transformation,[],[f32]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X0)
| ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_50,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,X0,initial_FM_EP(X0))
| ~ environment(X0)
| ~ in_environment(X0,initial_FM_EP(X0)) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(X1,initial_FM_EP(X0))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))
| decreases(difference(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3)))
| ~ environment(X1)
| ~ greater_or_equal(X3,X0)
| ~ greater_or_equal(X2,X3)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_54,plain,
! [X0: $i] :
( greater_or_equal(initial_FM_EP(X0),start_time(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( in_environment(X1,X0)
| ~ environment(X1)
| ~ greater(X2,X0)
| ~ in_environment(X1,X2)
| ~ greater_or_equal(X0,start_time(X1)) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( greater(X0,X1)
| ( X0 = X1 )
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_58,plain,
! [X0: $i] :
( greater(disbanding_rate(first_movers,initial_FM_EP(X0)),disbanding_rate(efficient_producers,initial_FM_EP(X0)))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subpopulations(first_movers,efficient_producers,X0,X3)
| ~ environment(X0)
| ~ greater_or_equal(X3,X1)
| ~ greater_or_equal(X2,X3)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_60,negated_conjecture,
~ greater(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1)),
inference(cnf_transformation,[],[f46]) ).
tcf(c_61,negated_conjecture,
environment(sK0),
inference(cnf_transformation,[],[f45]) ).
tcf(c_62,negated_conjecture,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f44]) ).
tcf(c_282,plain,
! [X0: $i,X1: $i,X2: $i] :
( in_environment(X0,X1)
| ~ greater(X2,X1)
| ~ in_environment(X0,X2)
| ~ greater_or_equal(X1,start_time(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_61]) ).
tcf(c_283,plain,
! [X0: $i,X1: $i] :
( in_environment(sK0,X0)
| ~ in_environment(sK0,X1)
| ~ greater(X1,X0)
| ~ greater_or_equal(X0,start_time(sK0)) ),
inference(unflattening,[status(thm)],[c_282]) ).
tcf(c_296,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))
| decreases(difference(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3)))
| ~ greater_or_equal(X3,X1)
| ~ greater_or_equal(X2,X3)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_61]) ).
tcf(c_297,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))
| decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)))
| ~ greater_or_equal(X2,X0)
| ~ greater_or_equal(X1,X2)
| ~ subpopulations(first_movers,efficient_producers,sK0,X1)
| ~ greater(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)) ),
inference(unflattening,[status(thm)],[c_296]) ).
tcf(c_316,plain,
! [X0: $i,X1: $i] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_61]) ).
tcf(c_317,plain,
! [X0: $i] :
( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
inference(unflattening,[status(thm)],[c_316]) ).
tcf(c_325,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater_or_equal(X3,X1)
| ~ greater_or_equal(X2,X3)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_61]) ).
tcf(c_326,plain,
! [X0: $i,X1: $i,X2: $i] :
( subpopulations(first_movers,efficient_producers,sK0,X2)
| ~ greater_or_equal(X2,X0)
| ~ greater_or_equal(X1,X2)
| ~ subpopulations(first_movers,efficient_producers,sK0,X1)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(unflattening,[status(thm)],[c_325]) ).
tcf(c_342,plain,
! [X0: $i] :
( greater(disbanding_rate(first_movers,initial_FM_EP(X0)),disbanding_rate(efficient_producers,initial_FM_EP(X0)))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_61]) ).
tcf(c_343,plain,
greater(disbanding_rate(first_movers,initial_FM_EP(sK0)),disbanding_rate(efficient_producers,initial_FM_EP(sK0))),
inference(unflattening,[status(thm)],[c_342]) ).
tcf(c_347,plain,
! [X0: $i] :
( greater_or_equal(initial_FM_EP(X0),start_time(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_61]) ).
tcf(c_348,plain,
greater_or_equal(initial_FM_EP(sK0),start_time(sK0)),
inference(unflattening,[status(thm)],[c_347]) ).
tcf(c_352,plain,
! [X0: $i,X1: $i] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_61]) ).
tcf(c_353,plain,
! [X0: $i] :
( in_environment(sK0,X0)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(unflattening,[status(thm)],[c_352]) ).
tcf(c_361,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(X1,initial_FM_EP(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_61]) ).
tcf(c_362,plain,
! [X0: $i] :
( greater_or_equal(X0,initial_FM_EP(sK0))
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(unflattening,[status(thm)],[c_361]) ).
tcf(c_370,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,X0,initial_FM_EP(X0))
| ~ in_environment(X0,initial_FM_EP(X0))
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_61]) ).
tcf(c_371,plain,
( subpopulations(first_movers,efficient_producers,sK0,initial_FM_EP(sK0))
| ~ in_environment(sK0,initial_FM_EP(sK0)) ),
inference(unflattening,[status(thm)],[c_370]) ).
tcf(c_595,definition,
iPr_def_10 = initial_FM_EP(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_596,definition,
iPr_def_11 = start_time(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_597,definition,
iPr_def_12 = disbanding_rate(first_movers,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_598,definition,
iPr_def_13 = disbanding_rate(efficient_producers,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_599,definition,
iPr_def_14 = disbanding_rate(first_movers,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_600,definition,
iPr_def_15 = disbanding_rate(efficient_producers,sK1),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_601,plain,
( subpopulations(first_movers,efficient_producers,sK0,iPr_def_10)
| ~ in_environment(sK0,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_371,c_595]) ).
tcf(c_602,plain,
! [X0: $i] :
( greater_or_equal(X0,iPr_def_10)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(demodulation,[status(thm)],[c_362]) ).
tcf(c_603,plain,
! [X0: $i] :
( in_environment(sK0,X0)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(demodulation,[status(thm)],[c_353]) ).
tcf(c_604,plain,
greater_or_equal(iPr_def_10,iPr_def_11),
inference(demodulation,[status(thm)],[c_348,c_596]) ).
tcf(c_605,plain,
greater(iPr_def_12,iPr_def_13),
inference(demodulation,[status(thm)],[c_343,c_598,c_597]) ).
tcf(c_606,plain,
! [X0: $i,X1: $i,X2: $i] :
( subpopulations(first_movers,efficient_producers,sK0,X2)
| ~ greater_or_equal(X2,X0)
| ~ greater_or_equal(X1,X2)
| ~ subpopulations(first_movers,efficient_producers,sK0,X1)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(demodulation,[status(thm)],[c_326]) ).
tcf(c_607,plain,
! [X0: $i] :
( ~ subpopulations(first_movers,efficient_producers,sK0,X0)
| ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
inference(demodulation,[status(thm)],[c_317]) ).
tcf(c_608,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))
| decreases(difference(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)))
| ~ greater_or_equal(X2,X0)
| ~ greater_or_equal(X1,X2)
| ~ subpopulations(first_movers,efficient_producers,sK0,X1)
| ~ greater(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)) ),
inference(demodulation,[status(thm)],[c_297]) ).
tcf(c_609,plain,
! [X0: $i,X1: $i] :
( in_environment(sK0,X1)
| ~ greater_or_equal(X1,iPr_def_11)
| ~ in_environment(sK0,X0)
| ~ greater(X0,X1) ),
inference(demodulation,[status(thm)],[c_283]) ).
tcf(c_610,negated_conjecture,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(demodulation,[status(thm)],[c_62]) ).
tcf(c_611,negated_conjecture,
~ greater(iPr_def_14,iPr_def_15),
inference(demodulation,[status(thm)],[c_60,c_600,c_599]) ).
tcf(c_935,plain,
greater_or_equal(sK1,iPr_def_10),
inference(superposition,[status(thm)],[c_610,c_602]) ).
tcf(c_936,plain,
( greater_or_equal(iPr_def_10,iPr_def_10)
| ~ in_environment(sK0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_601,c_602]) ).
tcf(c_943,plain,
in_environment(sK0,sK1),
inference(superposition,[status(thm)],[c_610,c_603]) ).
tcf(c_966,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,iPr_def_10)
| ~ decreases(difference(disbanding_rate(first_movers,iPr_def_10),iPr_def_13)) ),
inference(superposition,[status(thm)],[c_598,c_607]) ).
tcf(c_967,plain,
( ~ decreases(difference(iPr_def_12,iPr_def_13))
| ~ subpopulations(first_movers,efficient_producers,sK0,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_966,c_597]) ).
tcf(c_997,plain,
! [X0: $i,X1: $i] :
( subpopulations(first_movers,efficient_producers,sK0,X1)
| ~ greater_or_equal(sK1,X1)
| ~ greater_or_equal(X1,X0)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(superposition,[status(thm)],[c_610,c_606]) ).
tcf(c_1016,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sK0,X0)
| ~ greater_or_equal(sK1,X0)
| ~ greater_or_equal(X0,sK1) ),
inference(superposition,[status(thm)],[c_610,c_997]) ).
tcf(c_1034,plain,
! [X0: $i,X1: $i] :
( subpopulations(first_movers,efficient_producers,sK0,X0)
| ~ greater_or_equal(sK1,X1)
| ~ greater_or_equal(sK1,X0)
| ~ greater_or_equal(X1,sK1)
| ~ greater_or_equal(X0,X1) ),
inference(superposition,[status(thm)],[c_1016,c_997]) ).
tcf(c_1079,plain,
( greater(sK1,iPr_def_10)
| ( sK1 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_935,c_57]) ).
tcf(c_1103,plain,
( in_environment(sK0,iPr_def_10)
| ( sK1 = iPr_def_10 )
| ~ greater_or_equal(iPr_def_10,iPr_def_11)
| ~ in_environment(sK0,sK1) ),
inference(superposition,[status(thm)],[c_1079,c_609]) ).
tcf(c_1107,plain,
( in_environment(sK0,iPr_def_10)
| ( sK1 = iPr_def_10 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1103,c_604,c_943]) ).
tcf(c_1115,plain,
( ~ greater_or_equal(iPr_def_10,sK1)
| ~ greater_or_equal(sK1,iPr_def_10)
| ~ decreases(difference(iPr_def_12,iPr_def_13)) ),
inference(superposition,[status(thm)],[c_1016,c_967]) ).
tcf(c_1119,plain,
( ~ greater_or_equal(iPr_def_10,sK1)
| ~ decreases(difference(iPr_def_12,iPr_def_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1115,c_935]) ).
tcf(c_1126,plain,
( greater_or_equal(iPr_def_10,iPr_def_10)
| ( sK1 = iPr_def_10 ) ),
inference(superposition,[status(thm)],[c_1107,c_936]) ).
tcf(c_1185,plain,
( subpopulations(first_movers,efficient_producers,sK0,iPr_def_10)
| ( sK1 = iPr_def_10 )
| ~ greater_or_equal(iPr_def_10,sK1)
| ~ greater_or_equal(sK1,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1126,c_1034]) ).
tcf(c_1186,plain,
( subpopulations(first_movers,efficient_producers,sK0,iPr_def_10)
| ( sK1 = iPr_def_10 )
| ~ greater_or_equal(iPr_def_10,sK1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1185,c_935]) ).
tcf(c_1194,plain,
( subpopulations(first_movers,efficient_producers,sK0,iPr_def_10)
| ( sK1 = iPr_def_10 ) ),
inference(global_subsumption_just,[status(thm)],[c_1186,c_601,c_1107]) ).
tcf(c_1204,plain,
( ( sK1 = iPr_def_10 )
| ~ decreases(difference(iPr_def_12,iPr_def_13)) ),
inference(superposition,[status(thm)],[c_1194,c_967]) ).
tcf(c_1384,plain,
! [X0: $i,X1: $i] :
( greater(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))
| decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ greater_or_equal(X1,iPr_def_10)
| ~ greater_or_equal(X0,X1)
| ~ greater(disbanding_rate(first_movers,iPr_def_10),iPr_def_13)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(superposition,[status(thm)],[c_598,c_608]) ).
tcf(c_1385,plain,
! [X0: $i,X1: $i] :
( greater(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))
| decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ greater(iPr_def_12,iPr_def_13)
| ~ greater_or_equal(X1,iPr_def_10)
| ~ greater_or_equal(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(light_normalisation,[status(thm)],[c_1384,c_597]) ).
tcf(c_1386,plain,
! [X0: $i,X1: $i] :
( greater(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))
| decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ greater_or_equal(X1,iPr_def_10)
| ~ greater_or_equal(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1385,c_605]) ).
tcf(c_1408,plain,
( greater(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))
| decreases(difference(disbanding_rate(first_movers,iPr_def_10),disbanding_rate(efficient_producers,iPr_def_10)))
| ~ greater_or_equal(iPr_def_10,iPr_def_10)
| ~ subpopulations(first_movers,efficient_producers,sK0,sK1) ),
inference(superposition,[status(thm)],[c_935,c_1386]) ).
tcf(c_1410,plain,
( greater(iPr_def_14,iPr_def_15)
| decreases(difference(iPr_def_12,iPr_def_13))
| ~ greater_or_equal(iPr_def_10,iPr_def_10)
| ~ subpopulations(first_movers,efficient_producers,sK0,sK1) ),
inference(light_normalisation,[status(thm)],[c_1408,c_597,c_598,c_599,c_600]) ).
tcf(c_1411,plain,
( decreases(difference(iPr_def_12,iPr_def_13))
| ~ greater_or_equal(iPr_def_10,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1410,c_611,c_610]) ).
tcf(c_1422,plain,
( ( sK1 = iPr_def_10 )
| ~ greater_or_equal(iPr_def_10,iPr_def_10) ),
inference(superposition,[status(thm)],[c_1411,c_1204]) ).
tcf(c_1438,plain,
sK1 = iPr_def_10,
inference(global_subsumption_just,[status(thm)],[c_1422,c_1126,c_1422]) ).
tcf(c_1447,plain,
( ~ greater_or_equal(iPr_def_10,iPr_def_10)
| ~ decreases(difference(iPr_def_12,iPr_def_13)) ),
inference(demodulation,[status(thm)],[c_1119,c_1438]) ).
tcf(c_1455,plain,
greater_or_equal(iPr_def_10,iPr_def_10),
inference(demodulation,[status(thm)],[c_935,c_1438]) ).
tcf(c_1459,plain,
~ decreases(difference(iPr_def_12,iPr_def_13)),
inference(forward_subsumption_resolution,[status(thm)],[c_1447,c_1455]) ).
tcf(c_1484,plain,
decreases(difference(iPr_def_12,iPr_def_13)),
inference(backward_subsumption_resolution,[status(thm)],[c_1411,c_1455]) ).
tcf(c_1485,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1484,c_1459]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT020+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/10.39 % Computer : n019.cluster.edu
% 0.12/10.39 % Model : x86_64 x86_64
% 0.12/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.39 % Memory : 8046.5625MB
% 0.12/10.39 % OS : Linux 6.8.0-71-generic
% 0.12/10.39 % CPULimit : 300
% 0.12/10.39 % WCLimit : 300
% 0.12/10.39 % DateTime : Thu Sep 24 01:02:01 UTC 2026
% 0.12/10.39 % CPUTime :
% 0.12/10.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/10.43 Running first-order theorem proving
% 0.16/10.43 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/10.44
% 0.16/10.44 % ======== iProver multi-core TPTP/SMT =========
% 0.16/10.44
% 0.16/10.44 % Detected problem language: tptp
% 0.16/10.46 % Proving...
% 2.29/11.30 % SZS status Started for theBenchmark.p
% 2.29/11.30 % SZS status Theorem for theBenchmark.p
% 2.29/11.30
% 2.29/11.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.29/11.30
% 2.29/11.30 % ------ iProver source info
% 2.29/11.30
% 2.29/11.30 % git: date: 2026-07-19 20:42:38 +0200
% 2.29/11.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.29/11.30 % git: non_committed_changes: false
% 2.29/11.30
% 2.29/11.30 % ------ Parsing...
% 2.29/11.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.29/11.30
% 2.29/11.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.29/11.30
% 2.29/11.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.29/11.30
% 2.29/11.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.29/11.30 % ------ Proving...
% 2.29/11.30 % ------ Problem Properties
% 2.29/11.30
% 2.29/11.30 %
% 2.29/11.30 % clauses 19
% 2.29/11.30 % conjectures 2
% 2.29/11.30 % EPR 11
% 2.29/11.30 % Horn 17
% 2.29/11.30 % unary 10
% 2.29/11.30 % binary 4
% 2.29/11.30 % lits 39
% 2.29/11.30 % lits eq 7
% 2.29/11.30 % fd_pure 0
% 2.29/11.30 % fd_pseudo 0
% 2.29/11.30 % fd_cond 0
% 2.29/11.30 % fd_pseudo_cond 1
% 2.29/11.30 % AC symbols 0
% 2.29/11.30
% 2.29/11.30 % ------ Schedule dynamic 5 is on
% 2.29/11.30
% 2.29/11.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.29/11.30
% 2.29/11.30
% 2.29/11.30 % ------
% 2.29/11.30 % Current options:
% 2.29/11.30 % ------
% 2.29/11.30
% 2.29/11.30
% 2.29/11.30 %
% 2.29/11.30
% 2.29/11.30 % ------ Proving...
% 2.29/11.30 %
% 2.29/11.30
% 2.29/11.30 % SZS status Theorem for theBenchmark.p
% 2.29/11.30
% 2.29/11.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.29/11.31
% 2.29/11.31
%------------------------------------------------------------------------------