%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT020-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n012.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 : Unsatisfiable 0.27s 1.09s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 20
% Syntax : Number of formulae : 97 ( 25 unt; 6 def)
% Number of atoms : 371 ( 31 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 333 ( 162 ~; 171 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 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 : 104 ( 0 sgn 104 !; 0 ?; 79 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_22) ).
fof(f2,axiom,
! [X0] :
( subpopulations(first_movers,efficient_producers,X0,initial_FM_EP(X0))
| ~ in_environment(X0,initial_FM_EP(X0))
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_point_23) ).
fof(f3,axiom,
! [X0,X1] :
( greater_or_equal(X1,initial_FM_EP(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_point_24) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( 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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_function_difference_25) ).
fof(f5,axiom,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occurs_26) ).
fof(f6,axiom,
! [X0] :
( greater_or_equal(initial_FM_EP(X0),start_time(X0))
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_initial_time_27) ).
fof(f7,axiom,
! [X2,X0,X1] :
( in_environment(X0,X1)
| ~ in_environment(X0,X2)
| ~ greater(X2,X1)
| ~ greater_or_equal(X1,start_time(X0))
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_times_in_order_28) ).
fof(f8,axiom,
! [X2,X0,X1] :
( greater(X0,X2)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_transitivity_29) ).
fof(f9,axiom,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_30) ).
fof(f10,axiom,
! [X0] :
( greater(disbanding_rate(first_movers,initial_FM_EP(X0)),disbanding_rate(efficient_producers,initial_FM_EP(X0)))
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a8_31) ).
fof(f11,axiom,
! [X2,X3,X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,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) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a10_32) ).
fof(f12,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l2_33) ).
fof(f13,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l2_34) ).
fof(f14,negated_conjecture,
~ greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l2_35) ).
tcf(c_63,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,[],[f1]) ).
tcf(c_64,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,[],[f2]) ).
tcf(c_65,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,[],[f3]) ).
tcf(c_66,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,[],[f4]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_68,plain,
! [X0: $i] :
( greater_or_equal(initial_FM_EP(X0),start_time(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_69,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,[],[f7]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(X0,X2)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( greater(X0,X1)
| ( X0 = X1 )
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_72,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,[],[f10]) ).
tcf(c_73,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,[],[f11]) ).
tcf(c_74,negated_conjecture,
environment(sk1),
inference(cnf_transformation,[],[f12]) ).
tcf(c_75,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(cnf_transformation,[],[f13]) ).
tcf(c_76,negated_conjecture,
~ greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)),
inference(cnf_transformation,[],[f14]) ).
tcf(c_296,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 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_73,c_74]) ).
tcf(c_297,plain,
! [X0: $i,X1: $i,X2: $i] :
( subpopulations(first_movers,efficient_producers,sk1,X2)
| ~ greater_or_equal(X2,X0)
| ~ greater_or_equal(X1,X2)
| ~ subpopulations(first_movers,efficient_producers,sk1,X1)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(unflattening,[status(thm)],[c_296]) ).
tcf(c_313,plain,
! [X0: $i] :
( greater(disbanding_rate(first_movers,initial_FM_EP(X0)),disbanding_rate(efficient_producers,initial_FM_EP(X0)))
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_72,c_74]) ).
tcf(c_314,plain,
greater(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1))),
inference(unflattening,[status(thm)],[c_313]) ).
tcf(c_318,plain,
! [X0: $i] :
( greater_or_equal(initial_FM_EP(X0),start_time(X0))
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_68,c_74]) ).
tcf(c_319,plain,
greater_or_equal(initial_FM_EP(sk1),start_time(sk1)),
inference(unflattening,[status(thm)],[c_318]) ).
tcf(c_323,plain,
! [X0: $i,X1: $i] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_67,c_74]) ).
tcf(c_324,plain,
! [X0: $i] :
( in_environment(sk1,X0)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(unflattening,[status(thm)],[c_323]) ).
tcf(c_332,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(X1,initial_FM_EP(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_74]) ).
tcf(c_333,plain,
! [X0: $i] :
( greater_or_equal(X0,initial_FM_EP(sk1))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(unflattening,[status(thm)],[c_332]) ).
tcf(c_341,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,X0,initial_FM_EP(X0))
| ~ in_environment(X0,initial_FM_EP(X0))
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_64,c_74]) ).
tcf(c_342,plain,
( subpopulations(first_movers,efficient_producers,sk1,initial_FM_EP(sk1))
| ~ in_environment(sk1,initial_FM_EP(sk1)) ),
inference(unflattening,[status(thm)],[c_341]) ).
tcf(c_349,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 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_69,c_74]) ).
tcf(c_350,plain,
! [X0: $i,X1: $i] :
( in_environment(sk1,X0)
| ~ in_environment(sk1,X1)
| ~ greater(X1,X0)
| ~ greater_or_equal(X0,start_time(sk1)) ),
inference(unflattening,[status(thm)],[c_349]) ).
tcf(c_363,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 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_74]) ).
tcf(c_364,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,sk1,X1)
| ~ greater(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)) ),
inference(unflattening,[status(thm)],[c_363]) ).
tcf(c_383,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 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_63,c_74]) ).
tcf(c_384,plain,
! [X0: $i] :
( ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
inference(unflattening,[status(thm)],[c_383]) ).
tcf(c_609,definition,
iPr_def_10 = start_time(sk1),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_610,definition,
iPr_def_11 = initial_FM_EP(sk1),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_611,definition,
iPr_def_12 = disbanding_rate(first_movers,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_612,definition,
iPr_def_13 = disbanding_rate(efficient_producers,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_613,definition,
iPr_def_14 = disbanding_rate(first_movers,sk2),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_614,definition,
iPr_def_15 = disbanding_rate(efficient_producers,sk2),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_615,plain,
! [X0: $i] :
( ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0))) ),
inference(demodulation,[status(thm)],[c_384]) ).
tcf(c_616,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,sk1,X1)
| ~ greater(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)) ),
inference(demodulation,[status(thm)],[c_364]) ).
tcf(c_617,plain,
! [X0: $i,X1: $i] :
( in_environment(sk1,X1)
| ~ greater_or_equal(X1,iPr_def_10)
| ~ in_environment(sk1,X0)
| ~ greater(X0,X1) ),
inference(demodulation,[status(thm)],[c_350,c_609]) ).
tcf(c_618,plain,
( subpopulations(first_movers,efficient_producers,sk1,iPr_def_11)
| ~ in_environment(sk1,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_342,c_610]) ).
tcf(c_619,plain,
! [X0: $i] :
( greater_or_equal(X0,iPr_def_11)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(demodulation,[status(thm)],[c_333]) ).
tcf(c_620,plain,
! [X0: $i] :
( in_environment(sk1,X0)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(demodulation,[status(thm)],[c_324]) ).
tcf(c_621,plain,
greater_or_equal(iPr_def_11,iPr_def_10),
inference(demodulation,[status(thm)],[c_319]) ).
tcf(c_622,plain,
greater(iPr_def_12,iPr_def_13),
inference(demodulation,[status(thm)],[c_314,c_612,c_611]) ).
tcf(c_623,plain,
! [X0: $i,X1: $i,X2: $i] :
( subpopulations(first_movers,efficient_producers,sk1,X2)
| ~ greater_or_equal(X2,X0)
| ~ greater_or_equal(X1,X2)
| ~ subpopulations(first_movers,efficient_producers,sk1,X1)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(demodulation,[status(thm)],[c_297]) ).
tcf(c_624,negated_conjecture,
~ greater(iPr_def_14,iPr_def_15),
inference(demodulation,[status(thm)],[c_76,c_614,c_613]) ).
tcf(c_625,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(demodulation,[status(thm)],[c_75]) ).
tcf(c_949,plain,
greater_or_equal(sk2,iPr_def_11),
inference(superposition,[status(thm)],[c_625,c_619]) ).
tcf(c_950,plain,
( greater_or_equal(iPr_def_11,iPr_def_11)
| ~ in_environment(sk1,iPr_def_11) ),
inference(superposition,[status(thm)],[c_618,c_619]) ).
tcf(c_957,plain,
in_environment(sk1,sk2),
inference(superposition,[status(thm)],[c_625,c_620]) ).
tcf(c_980,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1,iPr_def_11)
| ~ decreases(difference(disbanding_rate(first_movers,iPr_def_11),iPr_def_13)) ),
inference(superposition,[status(thm)],[c_612,c_615]) ).
tcf(c_981,plain,
( ~ decreases(difference(iPr_def_12,iPr_def_13))
| ~ subpopulations(first_movers,efficient_producers,sk1,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_980,c_611]) ).
tcf(c_1011,plain,
! [X0: $i,X1: $i] :
( subpopulations(first_movers,efficient_producers,sk1,X1)
| ~ greater_or_equal(sk2,X1)
| ~ greater_or_equal(X1,X0)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(superposition,[status(thm)],[c_625,c_623]) ).
tcf(c_1030,plain,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ greater_or_equal(sk2,X0)
| ~ greater_or_equal(X0,sk2) ),
inference(superposition,[status(thm)],[c_625,c_1011]) ).
tcf(c_1048,plain,
! [X0: $i,X1: $i] :
( subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ greater_or_equal(sk2,X1)
| ~ greater_or_equal(sk2,X0)
| ~ greater_or_equal(X1,sk2)
| ~ greater_or_equal(X0,X1) ),
inference(superposition,[status(thm)],[c_1030,c_1011]) ).
tcf(c_1092,plain,
( greater(iPr_def_11,iPr_def_10)
| ( iPr_def_10 = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_621,c_71]) ).
tcf(c_1093,plain,
( greater(sk2,iPr_def_11)
| ( sk2 = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_949,c_71]) ).
tcf(c_1116,plain,
( in_environment(sk1,iPr_def_11)
| ( sk2 = iPr_def_11 )
| ~ greater_or_equal(iPr_def_11,iPr_def_10)
| ~ in_environment(sk1,sk2) ),
inference(superposition,[status(thm)],[c_1093,c_617]) ).
tcf(c_1117,plain,
! [X0: $i] :
( greater(sk2,X0)
| ( sk2 = iPr_def_11 )
| ~ greater(iPr_def_11,X0) ),
inference(superposition,[status(thm)],[c_1093,c_70]) ).
tcf(c_1121,plain,
( in_environment(sk1,iPr_def_11)
| ( sk2 = iPr_def_11 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1116,c_621,c_957]) ).
tcf(c_1129,plain,
( ~ greater_or_equal(iPr_def_11,sk2)
| ~ greater_or_equal(sk2,iPr_def_11)
| ~ decreases(difference(iPr_def_12,iPr_def_13)) ),
inference(superposition,[status(thm)],[c_1030,c_981]) ).
tcf(c_1133,plain,
( ~ greater_or_equal(iPr_def_11,sk2)
| ~ decreases(difference(iPr_def_12,iPr_def_13)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1129,c_949]) ).
tcf(c_1140,plain,
( greater_or_equal(iPr_def_11,iPr_def_11)
| ( sk2 = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_1121,c_950]) ).
tcf(c_1199,plain,
( subpopulations(first_movers,efficient_producers,sk1,iPr_def_11)
| ( sk2 = iPr_def_11 )
| ~ greater_or_equal(iPr_def_11,sk2)
| ~ greater_or_equal(sk2,iPr_def_11) ),
inference(superposition,[status(thm)],[c_1140,c_1048]) ).
tcf(c_1200,plain,
( subpopulations(first_movers,efficient_producers,sk1,iPr_def_11)
| ( sk2 = iPr_def_11 )
| ~ greater_or_equal(iPr_def_11,sk2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1199,c_949]) ).
tcf(c_1208,plain,
( subpopulations(first_movers,efficient_producers,sk1,iPr_def_11)
| ( sk2 = iPr_def_11 ) ),
inference(global_subsumption_just,[status(thm)],[c_1200,c_618,c_1121]) ).
tcf(c_1218,plain,
( ( sk2 = iPr_def_11 )
| ~ decreases(difference(iPr_def_12,iPr_def_13)) ),
inference(superposition,[status(thm)],[c_1208,c_981]) ).
tcf(c_1464,plain,
( greater(sk2,iPr_def_10)
| ( iPr_def_10 = iPr_def_11 )
| ( sk2 = iPr_def_11 ) ),
inference(superposition,[status(thm)],[c_1092,c_1117]) ).
tcf(c_1533,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_11)
| ~ greater_or_equal(X0,X1)
| ~ greater(disbanding_rate(first_movers,iPr_def_11),iPr_def_13)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(superposition,[status(thm)],[c_612,c_616]) ).
tcf(c_1534,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_11)
| ~ greater_or_equal(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(light_normalisation,[status(thm)],[c_1533,c_611]) ).
tcf(c_1535,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_11)
| ~ greater_or_equal(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1534,c_622]) ).
tcf(c_1854,plain,
( greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))
| decreases(difference(disbanding_rate(first_movers,iPr_def_11),disbanding_rate(efficient_producers,iPr_def_11)))
| ~ greater_or_equal(iPr_def_11,iPr_def_11)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2) ),
inference(superposition,[status(thm)],[c_949,c_1535]) ).
tcf(c_1856,plain,
( greater(iPr_def_14,iPr_def_15)
| decreases(difference(iPr_def_12,iPr_def_13))
| ~ greater_or_equal(iPr_def_11,iPr_def_11)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2) ),
inference(light_normalisation,[status(thm)],[c_1854,c_611,c_612,c_613,c_614]) ).
tcf(c_1857,plain,
( decreases(difference(iPr_def_12,iPr_def_13))
| ~ greater_or_equal(iPr_def_11,iPr_def_11) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1856,c_624,c_625]) ).
tcf(c_1866,plain,
( ( sk2 = iPr_def_11 )
| ~ greater_or_equal(iPr_def_11,iPr_def_11) ),
inference(superposition,[status(thm)],[c_1857,c_1218]) ).
tcf(c_1882,plain,
sk2 = iPr_def_11,
inference(global_subsumption_just,[status(thm)],[c_1464,c_1140,c_1866]) ).
tcf(c_1903,plain,
( ~ greater_or_equal(iPr_def_11,iPr_def_11)
| ~ decreases(difference(iPr_def_12,iPr_def_13)) ),
inference(demodulation,[status(thm)],[c_1133,c_1882]) ).
tcf(c_1911,plain,
greater_or_equal(iPr_def_11,iPr_def_11),
inference(demodulation,[status(thm)],[c_949,c_1882]) ).
tcf(c_1915,plain,
~ decreases(difference(iPr_def_12,iPr_def_13)),
inference(forward_subsumption_resolution,[status(thm)],[c_1903,c_1911]) ).
tcf(c_1954,plain,
decreases(difference(iPr_def_12,iPr_def_13)),
inference(backward_subsumption_resolution,[status(thm)],[c_1857,c_1911]) ).
tcf(c_1955,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1954,c_1915]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : MGT020-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.29 % Computer : n012.cluster.edu
% 0.03/0.29 % Model : x86_64 x86_64
% 0.03/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.29 % Memory : 8046.5625MB
% 0.03/0.29 % OS : Linux 6.8.0-71-generic
% 0.03/0.29 % CPULimit : 300
% 0.03/0.29 % WCLimit : 300
% 0.03/0.29 % DateTime : Thu Sep 24 01:01:35 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.34
% 0.03/0.34 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.34
% 0.03/0.34 % Detected problem language: tptp
% 0.03/0.35 % Proving...
% 0.27/1.09 % SZS status Started for theBenchmark.p
% 0.27/1.09 % SZS status Unsatisfiable for theBenchmark.p
% 0.27/1.09
% 0.27/1.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.27/1.09
% 0.27/1.09 % ------ iProver source info
% 0.27/1.09
% 0.27/1.09 % git: date: 2026-07-19 20:42:38 +0200
% 0.27/1.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.27/1.09 % git: non_committed_changes: false
% 0.27/1.09
% 0.27/1.09 % ------ Parsing...% successful
% 0.27/1.09
% 0.27/1.09
% 0.27/1.09 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.27/1.09
% 0.27/1.09 % ------ 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 %
% 0.27/1.09
% 0.27/1.09 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.27/1.09
% 0.27/1.09 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.27/1.09 % ------ Proving...
% 0.27/1.09 % ------ Problem Properties
% 0.27/1.09
% 0.27/1.09 %
% 0.27/1.09 % clauses 19
% 0.27/1.09 % conjectures 2
% 0.27/1.09 % EPR 11
% 0.27/1.09 % Horn 17
% 0.27/1.09 % unary 10
% 0.27/1.09 % binary 4
% 0.27/1.09 % lits 39
% 0.27/1.09 % lits eq 7
% 0.27/1.09 % fd_pure 0
% 0.27/1.09 % fd_pseudo 0
% 0.27/1.09 % fd_cond 0
% 0.27/1.09 % fd_pseudo_cond 1
% 0.27/1.09 % AC symbols 0
% 0.27/1.09
% 0.27/1.09 % ------ Schedule dynamic 5 is on
% 0.27/1.09
% 0.27/1.09 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.27/1.09
% 0.27/1.09
% 0.27/1.09 % ------
% 0.27/1.09 % Current options:
% 0.27/1.09 % ------
% 0.27/1.09
% 0.27/1.09
% 0.27/1.09 %
% 0.27/1.09
% 0.27/1.09 % ------ Proving...
% 0.27/1.09 %
% 0.27/1.09
% 0.27/1.09 % SZS status Unsatisfiable for theBenchmark.p
% 0.27/1.09
% 0.27/1.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.27/1.09
% 0.27/1.09
%------------------------------------------------------------------------------