%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT029-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 02:12:25 PM UTC 2026
% Result : Unsatisfiable 3.00s 0.98s
% Output : CNFRefutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 27
% Syntax : Number of formulae : 241 ( 13 unt; 0 def)
% Number of atoms : 968 ( 292 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 1269 ( 542 ~; 727 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 285 ( 0 sgn 285 !; 0 ?; 240 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( greater(X0,X2)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_transitivity_19) ).
fof(f2,axiom,
! [X2,X0,X1] :
( greater(X1,X2)
| X2 = X1
| greater(X2,X1)
| ~ in_environment(X0,X2)
| ~ in_environment(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_times_in_environment_20) ).
fof(f3,plain,
! [X2,X0,X1] :
( greater(X1,X2)
| X1 = X2
| greater(X2,X1)
| ~ in_environment(X0,X2)
| ~ in_environment(X0,X1) ),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X0,X1] :
( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_21) ).
fof(f5,axiom,
! [X0,X1] :
( greater_or_equal(X0,X1)
| ~ greater(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_22) ).
fof(f7,axiom,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| growth_rate(first_movers,X1) = zero
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l6_24) ).
fof(f8,axiom,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| growth_rate(first_movers,X1) = zero
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l6_25) ).
fof(f9,axiom,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(zero,growth_rate(efficient_producers,X1))
| growth_rate(first_movers,X1) = zero
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l6_26) ).
fof(f10,axiom,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(efficient_producers,X1))
| growth_rate(first_movers,X1) = zero
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l6_27) ).
fof(f11,axiom,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| growth_rate(efficient_producers,X1) = zero
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l6_28) ).
fof(f12,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| zero = growth_rate(efficient_producers,X1)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(reorient_equations,[],[f11]) ).
fof(f13,axiom,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| growth_rate(efficient_producers,X1) = zero
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l6_29) ).
fof(f14,plain,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| zero = growth_rate(efficient_producers,X1)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(reorient_equations,[],[f13]) ).
fof(f15,axiom,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(zero,growth_rate(efficient_producers,X1))
| growth_rate(efficient_producers,X1) = zero
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l6_30) ).
fof(f16,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(zero,growth_rate(efficient_producers,X1))
| zero = growth_rate(efficient_producers,X1)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,axiom,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(efficient_producers,X1))
| growth_rate(efficient_producers,X1) = zero
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l6_31) ).
fof(f18,plain,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(efficient_producers,X1))
| zero = growth_rate(efficient_producers,X1)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(reorient_equations,[],[f17]) ).
fof(f19,axiom,
! [X0] :
( in_environment(X0,sk1(X0))
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_32) ).
fof(f20,axiom,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_33) ).
fof(f21,axiom,
! [X0] :
( in_environment(X0,sk2(X0))
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4_34) ).
fof(f22,axiom,
! [X0] :
( greater_or_equal(sk2(X0),equilibrium(X0))
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a4_35) ).
fof(f23,negated_conjecture,
environment(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l11_36) ).
fof(f24,negated_conjecture,
stable(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l11_37) ).
fof(f25,negated_conjecture,
! [X0] :
( subpopulations(first_movers,efficient_producers,sk3,sk4(X0))
| ~ in_environment(sk3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l11_38) ).
fof(f26,negated_conjecture,
! [X0] :
( greater_or_equal(sk4(X0),X0)
| ~ in_environment(sk3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l11_39) ).
fof(f27,negated_conjecture,
! [X0] :
( ~ greater(zero,growth_rate(first_movers,sk4(X0)))
| ~ greater(growth_rate(efficient_producers,sk4(X0)),zero)
| ~ in_environment(sk3,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l11_40) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(X0,X2)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(X2,X1)
| greater(X1,X2)
| ( X1 = X2 )
| ~ in_environment(X0,X2)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( greater(X0,X1)
| ( X0 = X1 )
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| ( growth_rate(first_movers,X1) = zero )
| ~ environment(X0)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_77,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| ( growth_rate(first_movers,X1) = zero )
| ~ environment(X0)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_78,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(efficient_producers,X1))
| greater(growth_rate(efficient_producers,X1),zero)
| ( growth_rate(first_movers,X1) = zero )
| ~ environment(X0)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(efficient_producers,X1))
| greater(zero,growth_rate(first_movers,X1))
| ( growth_rate(first_movers,X1) = zero )
| ~ environment(X0)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_80,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| ( growth_rate(efficient_producers,X1) = zero )
| ~ environment(X0)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| ( growth_rate(efficient_producers,X1) = zero )
| ~ environment(X0)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_82,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(efficient_producers,X1))
| greater(growth_rate(efficient_producers,X1),zero)
| ( growth_rate(efficient_producers,X1) = zero )
| ~ environment(X0)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_83,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(efficient_producers,X1))
| greater(zero,growth_rate(first_movers,X1))
| ( growth_rate(efficient_producers,X1) = zero )
| ~ environment(X0)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_84,plain,
! [X0: $i] :
( in_environment(X0,sk1(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ stable(X0)
| ~ environment(X0)
| ~ greater_or_equal(X1,sk1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_86,plain,
! [X0: $i] :
( in_environment(X0,sk2(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_87,plain,
! [X0: $i] :
( greater_or_equal(sk2(X0),equilibrium(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_88,negated_conjecture,
environment(sk3),
inference(cnf_transformation,[],[f23]) ).
tcf(c_89,negated_conjecture,
stable(sk3),
inference(cnf_transformation,[],[f24]) ).
tcf(c_90,negated_conjecture,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sk3,sk4(X0))
| ~ in_environment(sk3,X0) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_91,negated_conjecture,
! [X0: $i] :
( greater_or_equal(sk4(X0),X0)
| ~ in_environment(sk3,X0) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_92,negated_conjecture,
! [X0: $i] :
( ~ in_environment(sk3,X0)
| ~ greater(zero,growth_rate(first_movers,sk4(X0)))
| ~ greater(growth_rate(efficient_producers,sk4(X0)),zero) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_291,plain,
! [X0: $i] :
( greater_or_equal(sk2(X0),equilibrium(X0))
| ~ environment(X0)
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_87,c_89]) ).
tcf(c_292,plain,
( greater_or_equal(sk2(sk3),equilibrium(sk3))
| ~ environment(sk3) ),
inference(unflattening,[status(thm)],[c_291]) ).
tcf(c_293,plain,
greater_or_equal(sk2(sk3),equilibrium(sk3)),
inference(global_subsumption_just,[status(thm)],[c_292,c_88,c_292]) ).
tcf(c_298,plain,
! [X0: $i] :
( in_environment(X0,sk2(X0))
| ~ environment(X0)
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_86,c_89]) ).
tcf(c_299,plain,
( in_environment(sk3,sk2(sk3))
| ~ environment(sk3) ),
inference(unflattening,[status(thm)],[c_298]) ).
tcf(c_305,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0)
| ~ greater_or_equal(X1,sk1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_85,c_89]) ).
tcf(c_306,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ environment(sk3)
| ~ greater_or_equal(X0,sk1(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0) ),
inference(unflattening,[status(thm)],[c_305]) ).
tcf(c_308,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0)
| ~ greater_or_equal(X0,sk1(sk3)) ),
inference(global_subsumption_just,[status(thm)],[c_306,c_88,c_306]) ).
tcf(c_309,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater_or_equal(X0,sk1(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0) ),
inference(renaming,[status(thm)],[c_308]) ).
tcf(c_320,plain,
! [X0: $i] :
( in_environment(X0,sk1(X0))
| ~ environment(X0)
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_84,c_89]) ).
tcf(c_321,plain,
( in_environment(sk3,sk1(sk3))
| ~ environment(sk3) ),
inference(unflattening,[status(thm)],[c_320]) ).
tcf(c_322,plain,
in_environment(sk3,sk1(sk3)),
inference(global_subsumption_just,[status(thm)],[c_321,c_88,c_321]) ).
tcf(c_333,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(efficient_producers,X1))
| greater(zero,growth_rate(first_movers,X1))
| ( growth_rate(efficient_producers,X1) = zero )
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_83,c_88]) ).
tcf(c_334,plain,
! [X0: $i] :
( greater(zero,growth_rate(efficient_producers,X0))
| greater(zero,growth_rate(first_movers,X0))
| ( growth_rate(efficient_producers,X0) = zero )
| ~ greater_or_equal(X0,equilibrium(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0) ),
inference(unflattening,[status(thm)],[c_333]) ).
tcf(c_351,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(efficient_producers,X1))
| greater(growth_rate(efficient_producers,X1),zero)
| ( growth_rate(efficient_producers,X1) = zero )
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_82,c_88]) ).
tcf(c_352,plain,
! [X0: $i] :
( greater(zero,growth_rate(efficient_producers,X0))
| greater(growth_rate(efficient_producers,X0),zero)
| ( growth_rate(efficient_producers,X0) = zero )
| ~ greater_or_equal(X0,equilibrium(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0) ),
inference(unflattening,[status(thm)],[c_351]) ).
tcf(c_369,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| ( growth_rate(efficient_producers,X1) = zero )
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_81,c_88]) ).
tcf(c_370,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| greater(growth_rate(first_movers,X0),zero)
| ( growth_rate(efficient_producers,X0) = zero )
| ~ greater_or_equal(X0,equilibrium(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0) ),
inference(unflattening,[status(thm)],[c_369]) ).
tcf(c_387,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| ( growth_rate(efficient_producers,X1) = zero )
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_80,c_88]) ).
tcf(c_388,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),zero)
| greater(growth_rate(first_movers,X0),zero)
| ( growth_rate(efficient_producers,X0) = zero )
| ~ greater_or_equal(X0,equilibrium(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0) ),
inference(unflattening,[status(thm)],[c_387]) ).
tcf(c_405,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(efficient_producers,X1))
| greater(zero,growth_rate(first_movers,X1))
| ( growth_rate(first_movers,X1) = zero )
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_79,c_88]) ).
tcf(c_406,plain,
! [X0: $i] :
( greater(zero,growth_rate(efficient_producers,X0))
| greater(zero,growth_rate(first_movers,X0))
| ( growth_rate(first_movers,X0) = zero )
| ~ greater_or_equal(X0,equilibrium(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0) ),
inference(unflattening,[status(thm)],[c_405]) ).
tcf(c_423,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(efficient_producers,X1))
| greater(growth_rate(efficient_producers,X1),zero)
| ( growth_rate(first_movers,X1) = zero )
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_78,c_88]) ).
tcf(c_424,plain,
! [X0: $i] :
( greater(zero,growth_rate(efficient_producers,X0))
| greater(growth_rate(efficient_producers,X0),zero)
| ( growth_rate(first_movers,X0) = zero )
| ~ greater_or_equal(X0,equilibrium(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0) ),
inference(unflattening,[status(thm)],[c_423]) ).
tcf(c_441,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| ( growth_rate(first_movers,X1) = zero )
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_77,c_88]) ).
tcf(c_442,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| greater(growth_rate(first_movers,X0),zero)
| ( growth_rate(first_movers,X0) = zero )
| ~ greater_or_equal(X0,equilibrium(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0) ),
inference(unflattening,[status(thm)],[c_441]) ).
tcf(c_459,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| ( growth_rate(first_movers,X1) = zero )
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_76,c_88]) ).
tcf(c_460,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),zero)
| greater(growth_rate(first_movers,X0),zero)
| ( growth_rate(first_movers,X0) = zero )
| ~ greater_or_equal(X0,equilibrium(sk3))
| ~ subpopulations(first_movers,efficient_producers,sk3,X0) ),
inference(unflattening,[status(thm)],[c_459]) ).
tcf(c_517,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| ( growth_rate(first_movers,X1) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(X1,equilibrium(sk3))
| ( sk3 != sk3 )
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( sk4(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_90,c_460]) ).
tcf(c_518,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,sk4(X0)),zero)
| greater(growth_rate(first_movers,sk4(X0)),zero)
| ( growth_rate(first_movers,sk4(X0)) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(unflattening,[status(thm)],[c_517]) ).
tcf(c_535,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| ( growth_rate(first_movers,X1) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(X1,equilibrium(sk3))
| ( sk3 != sk3 )
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( sk4(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_90,c_442]) ).
tcf(c_536,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,sk4(X0)))
| greater(growth_rate(first_movers,sk4(X0)),zero)
| ( growth_rate(first_movers,sk4(X0)) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(unflattening,[status(thm)],[c_535]) ).
tcf(c_538,plain,
! [X0: $i] :
( ~ greater_or_equal(sk4(X0),equilibrium(sk3))
| ~ in_environment(sk3,X0)
| ( growth_rate(first_movers,sk4(X0)) = zero )
| greater(growth_rate(first_movers,sk4(X0)),zero) ),
inference(global_subsumption_just,[status(thm)],[c_536,c_92,c_518,c_536]) ).
tcf(c_539,plain,
! [X0: $i] :
( greater(growth_rate(first_movers,sk4(X0)),zero)
| ( growth_rate(first_movers,sk4(X0)) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(renaming,[status(thm)],[c_538]) ).
tcf(c_553,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(efficient_producers,X1))
| greater(growth_rate(efficient_producers,X1),zero)
| ( growth_rate(first_movers,X1) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(X1,equilibrium(sk3))
| ( sk3 != sk3 )
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( sk4(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_90,c_424]) ).
tcf(c_554,plain,
! [X0: $i] :
( greater(zero,growth_rate(efficient_producers,sk4(X0)))
| greater(growth_rate(efficient_producers,sk4(X0)),zero)
| ( growth_rate(first_movers,sk4(X0)) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(unflattening,[status(thm)],[c_553]) ).
tcf(c_571,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(efficient_producers,X1))
| greater(zero,growth_rate(first_movers,X1))
| ( growth_rate(first_movers,X1) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(X1,equilibrium(sk3))
| ( sk3 != sk3 )
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( sk4(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_90,c_406]) ).
tcf(c_572,plain,
! [X0: $i] :
( greater(zero,growth_rate(efficient_producers,sk4(X0)))
| greater(zero,growth_rate(first_movers,sk4(X0)))
| ( growth_rate(first_movers,sk4(X0)) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(unflattening,[status(thm)],[c_571]) ).
tcf(c_574,plain,
! [X0: $i] :
( greater(zero,growth_rate(efficient_producers,sk4(X0)))
| ~ greater_or_equal(sk4(X0),equilibrium(sk3))
| ~ in_environment(sk3,X0)
| ( growth_rate(first_movers,sk4(X0)) = zero ) ),
inference(global_subsumption_just,[status(thm)],[c_572,c_92,c_554,c_572]) ).
tcf(c_575,plain,
! [X0: $i] :
( greater(zero,growth_rate(efficient_producers,sk4(X0)))
| ( growth_rate(first_movers,sk4(X0)) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(renaming,[status(thm)],[c_574]) ).
tcf(c_589,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| ( growth_rate(efficient_producers,X1) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(X1,equilibrium(sk3))
| ( sk3 != sk3 )
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( sk4(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_90,c_388]) ).
tcf(c_590,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,sk4(X0)),zero)
| greater(growth_rate(first_movers,sk4(X0)),zero)
| ( growth_rate(efficient_producers,sk4(X0)) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(unflattening,[status(thm)],[c_589]) ).
tcf(c_607,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| ( growth_rate(efficient_producers,X1) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(X1,equilibrium(sk3))
| ( sk3 != sk3 )
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( sk4(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_90,c_370]) ).
tcf(c_608,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,sk4(X0)))
| greater(growth_rate(first_movers,sk4(X0)),zero)
| ( growth_rate(efficient_producers,sk4(X0)) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(unflattening,[status(thm)],[c_607]) ).
tcf(c_610,plain,
! [X0: $i] :
( ~ greater_or_equal(sk4(X0),equilibrium(sk3))
| ~ in_environment(sk3,X0)
| ( growth_rate(efficient_producers,sk4(X0)) = zero )
| greater(growth_rate(first_movers,sk4(X0)),zero) ),
inference(global_subsumption_just,[status(thm)],[c_608,c_92,c_590,c_608]) ).
tcf(c_611,plain,
! [X0: $i] :
( greater(growth_rate(first_movers,sk4(X0)),zero)
| ( growth_rate(efficient_producers,sk4(X0)) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(renaming,[status(thm)],[c_610]) ).
tcf(c_625,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(efficient_producers,X1))
| greater(growth_rate(efficient_producers,X1),zero)
| ( growth_rate(efficient_producers,X1) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(X1,equilibrium(sk3))
| ( sk3 != sk3 )
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( sk4(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_90,c_352]) ).
tcf(c_626,plain,
! [X0: $i] :
( greater(zero,growth_rate(efficient_producers,sk4(X0)))
| greater(growth_rate(efficient_producers,sk4(X0)),zero)
| ( growth_rate(efficient_producers,sk4(X0)) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(unflattening,[status(thm)],[c_625]) ).
tcf(c_643,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(efficient_producers,X1))
| greater(zero,growth_rate(first_movers,X1))
| ( growth_rate(efficient_producers,X1) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(X1,equilibrium(sk3))
| ( sk3 != sk3 )
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( sk4(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_90,c_334]) ).
tcf(c_644,plain,
! [X0: $i] :
( greater(zero,growth_rate(efficient_producers,sk4(X0)))
| greater(zero,growth_rate(first_movers,sk4(X0)))
| ( growth_rate(efficient_producers,sk4(X0)) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(unflattening,[status(thm)],[c_643]) ).
tcf(c_646,plain,
! [X0: $i] :
( greater(zero,growth_rate(efficient_producers,sk4(X0)))
| ~ greater_or_equal(sk4(X0),equilibrium(sk3))
| ~ in_environment(sk3,X0)
| ( growth_rate(efficient_producers,sk4(X0)) = zero ) ),
inference(global_subsumption_just,[status(thm)],[c_644,c_92,c_626,c_644]) ).
tcf(c_647,plain,
! [X0: $i] :
( greater(zero,growth_rate(efficient_producers,sk4(X0)))
| ( growth_rate(efficient_producers,sk4(X0)) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(renaming,[status(thm)],[c_646]) ).
tcf(c_661,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(X1,sk1(sk3))
| ( sk3 != sk3 )
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( sk4(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_90,c_309]) ).
tcf(c_662,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,sk4(X0)),growth_rate(first_movers,sk4(X0)))
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(sk4(X0),sk1(sk3)) ),
inference(unflattening,[status(thm)],[c_661]) ).
tcf(c_708,plain,
! [X0: $i,X1: $i] :
( greater(X0,X1)
| ( X0 = X1 )
| ( sk2(sk3) != X0 )
| ( equilibrium(sk3) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_73,c_293]) ).
tcf(c_709,plain,
( greater(sk2(sk3),equilibrium(sk3))
| ( sk2(sk3) = equilibrium(sk3) ) ),
inference(unflattening,[status(thm)],[c_708]) ).
tcf(c_1616,plain,
! [X0: $i] : X0 = X0,
theory(equality) ).
tcf(c_1618,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X2 = X0 )
| ( X2 != X1 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1619,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( greater(X0,X2)
| ~ greater(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1620,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( in_environment(X0,X2)
| ~ in_environment(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1621,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( greater_or_equal(X0,X2)
| ~ greater_or_equal(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1624,plain,
! [X0: $i,X1: $i] :
( ( sk1(X0) = sk1(X1) )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_1630,plain,
zero = zero,
inference(instantiation,[status(thm)],[c_1616]) ).
tcf(c_1898,plain,
( greater(growth_rate(efficient_producers,sk4(sk2(sk3))),growth_rate(first_movers,sk4(sk2(sk3))))
| ~ in_environment(sk3,sk2(sk3))
| ~ greater_or_equal(sk4(sk2(sk3)),sk1(sk3)) ),
inference(instantiation,[status(thm)],[c_662]) ).
tcf(c_1903,plain,
( ~ in_environment(sk3,sk2(sk3))
| ~ greater(zero,growth_rate(first_movers,sk4(sk2(sk3))))
| ~ greater(growth_rate(efficient_producers,sk4(sk2(sk3))),zero) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_1904,plain,
( greater_or_equal(sk4(sk2(sk3)),sk2(sk3))
| ~ in_environment(sk3,sk2(sk3)) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_1907,plain,
( greater(growth_rate(efficient_producers,sk4(sk1(sk3))),growth_rate(first_movers,sk4(sk1(sk3))))
| ~ in_environment(sk3,sk1(sk3))
| ~ greater_or_equal(sk4(sk1(sk3)),sk1(sk3)) ),
inference(instantiation,[status(thm)],[c_662]) ).
tcf(c_1912,plain,
( ~ in_environment(sk3,sk1(sk3))
| ~ greater(zero,growth_rate(first_movers,sk4(sk1(sk3))))
| ~ greater(growth_rate(efficient_producers,sk4(sk1(sk3))),zero) ),
inference(instantiation,[status(thm)],[c_92]) ).
tcf(c_1913,plain,
( greater_or_equal(sk4(sk1(sk3)),sk1(sk3))
| ~ in_environment(sk3,sk1(sk3)) ),
inference(instantiation,[status(thm)],[c_91]) ).
tcf(c_1929,plain,
( greater_or_equal(sk4(sk2(sk3)),sk1(sk3))
| ~ greater(sk4(sk2(sk3)),sk1(sk3)) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_1930,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(sk4(sk2(sk3)),sk1(sk3))
| ~ greater_or_equal(X0,X1)
| ( sk1(sk3) != X1 )
| ( sk4(sk2(sk3)) != X0 ) ),
inference(instantiation,[status(thm)],[c_1621]) ).
tcf(c_1933,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(sk4(sk2(sk3)),equilibrium(sk3))
| ~ greater_or_equal(X0,X1)
| ( equilibrium(sk3) != X1 )
| ( sk4(sk2(sk3)) != X0 ) ),
inference(instantiation,[status(thm)],[c_1621]) ).
tcf(c_1941,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,sk4(sk2(sk3))))
| ~ greater(X1,X0)
| ( zero != X1 )
| ( growth_rate(first_movers,sk4(sk2(sk3))) != X0 ) ),
inference(instantiation,[status(thm)],[c_1619]) ).
tcf(c_1943,plain,
( greater(zero,growth_rate(first_movers,sk4(sk2(sk3))))
| ~ greater(zero,zero)
| ( zero != zero )
| ( growth_rate(first_movers,sk4(sk2(sk3))) != zero ) ),
inference(instantiation,[status(thm)],[c_1941]) ).
tcf(c_1953,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,sk4(sk1(sk3))))
| ~ greater(X1,X0)
| ( zero != X1 )
| ( growth_rate(first_movers,sk4(sk1(sk3))) != X0 ) ),
inference(instantiation,[status(thm)],[c_1619]) ).
tcf(c_1955,plain,
( greater(zero,growth_rate(first_movers,sk4(sk1(sk3))))
| ~ greater(zero,zero)
| ( zero != zero )
| ( growth_rate(first_movers,sk4(sk1(sk3))) != zero ) ),
inference(instantiation,[status(thm)],[c_1953]) ).
tcf(c_1958,plain,
sk3 = sk3,
inference(instantiation,[status(thm)],[c_1616]) ).
tcf(c_1966,plain,
! [X0: $i] :
( greater(sk4(sk2(sk3)),X0)
| ( sk4(sk2(sk3)) = X0 )
| ~ greater_or_equal(sk4(sk2(sk3)),X0) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_1968,plain,
! [X0: $i] :
( greater_or_equal(sk4(sk2(sk3)),sk1(sk3))
| ~ greater_or_equal(sk4(sk2(sk3)),X0)
| ( sk1(sk3) != X0 )
| ( sk4(sk2(sk3)) != sk4(sk2(sk3)) ) ),
inference(instantiation,[status(thm)],[c_1930]) ).
tcf(c_1979,plain,
! [X0: $i] :
( greater_or_equal(sk4(sk2(sk3)),equilibrium(sk3))
| ~ greater_or_equal(sk4(sk2(sk3)),X0)
| ( equilibrium(sk3) != X0 )
| ( sk4(sk2(sk3)) != sk4(sk2(sk3)) ) ),
inference(instantiation,[status(thm)],[c_1933]) ).
tcf(c_1990,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(first_movers,sk4(X0)),X1)
| ( growth_rate(first_movers,sk4(X0)) = zero )
| ~ in_environment(sk3,X0)
| ~ greater(zero,X1)
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(superposition,[status(thm)],[c_539,c_71]) ).
tcf(c_1991,plain,
! [X0: $i,X1: $i] :
( greater(zero,X1)
| ( growth_rate(first_movers,sk4(X0)) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(sk4(X0),equilibrium(sk3))
| ~ greater(growth_rate(efficient_producers,sk4(X0)),X1) ),
inference(superposition,[status(thm)],[c_575,c_71]) ).
tcf(c_1992,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,sk4(X0)),X1)
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(sk4(X0),sk1(sk3))
| ~ greater(growth_rate(first_movers,sk4(X0)),X1) ),
inference(superposition,[status(thm)],[c_662,c_71]) ).
tcf(c_2012,plain,
! [X0: $i] :
( greater(sk4(X0),X0)
| ( sk4(X0) = X0 )
| ~ in_environment(sk3,X0) ),
inference(superposition,[status(thm)],[c_91,c_73]) ).
tcf(c_2014,plain,
( greater(sk2(sk3),equilibrium(sk3))
| ( equilibrium(sk3) = sk2(sk3) ) ),
inference(superposition,[status(thm)],[c_293,c_73]) ).
tcf(c_2018,plain,
! [X0: $i] :
( greater(sk2(sk3),X0)
| ( equilibrium(sk3) = sk2(sk3) )
| ~ greater(equilibrium(sk3),X0) ),
inference(superposition,[status(thm)],[c_2014,c_71]) ).
tcf(c_2026,plain,
! [X0: $i,X1: $i] :
( greater(sk4(X0),X1)
| ( sk4(X0) = X0 )
| ~ in_environment(sk3,X0)
| ~ greater(X0,X1) ),
inference(superposition,[status(thm)],[c_2012,c_71]) ).
tcf(c_2056,plain,
( greater(sk4(sk2(sk3)),sk2(sk3))
| ( sk4(sk2(sk3)) = sk2(sk3) )
| ~ greater_or_equal(sk4(sk2(sk3)),sk2(sk3)) ),
inference(instantiation,[status(thm)],[c_1966]) ).
tcf(c_2057,plain,
! [X0: $i,X1: $i] :
( greater(zero,X1)
| ( growth_rate(efficient_producers,sk4(X0)) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(sk4(X0),equilibrium(sk3))
| ~ greater(growth_rate(efficient_producers,sk4(X0)),X1) ),
inference(superposition,[status(thm)],[c_647,c_71]) ).
tcf(c_2064,plain,
( greater_or_equal(sk4(sk2(sk3)),sk1(sk3))
| ~ greater_or_equal(sk4(sk2(sk3)),sk2(sk3))
| ( sk1(sk3) != sk2(sk3) )
| ( sk4(sk2(sk3)) != sk4(sk2(sk3)) ) ),
inference(instantiation,[status(thm)],[c_1968]) ).
tcf(c_2065,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(sk4(X0),X2)
| ( sk4(X0) = X0 )
| ~ in_environment(sk3,X0)
| ~ greater(X1,X2)
| ~ greater(X0,X1) ),
inference(superposition,[status(thm)],[c_2026,c_71]) ).
tcf(c_2066,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(sk4(X0),X1)
| ( sk4(X0) = X0 )
| ~ in_environment(sk3,X0)
| ~ greater(X0,X1) ),
inference(superposition,[status(thm)],[c_2026,c_74]) ).
tcf(c_2075,plain,
( greater_or_equal(sk4(sk2(sk3)),equilibrium(sk3))
| ~ greater_or_equal(sk4(sk2(sk3)),sk2(sk3))
| ( equilibrium(sk3) != sk2(sk3) )
| ( sk4(sk2(sk3)) != sk4(sk2(sk3)) ) ),
inference(instantiation,[status(thm)],[c_1979]) ).
tcf(c_2091,plain,
( greater(sk2(sk3),equilibrium(sk3))
| ( equilibrium(sk3) = sk2(sk3) ) ),
inference(superposition,[status(thm)],[c_293,c_73]) ).
tcf(c_2124,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,sk4(X0)),zero)
| ( growth_rate(efficient_producers,sk4(X0)) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(sk4(X0),sk1(sk3))
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(superposition,[status(thm)],[c_611,c_1992]) ).
tcf(c_2125,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,sk4(X0)),zero)
| ( growth_rate(first_movers,sk4(X0)) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(sk4(X0),sk1(sk3))
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(superposition,[status(thm)],[c_539,c_1992]) ).
tcf(c_2141,plain,
! [X0: $i] :
( greater(X0,sk1(sk3))
| greater(sk1(sk3),X0)
| ( sk1(sk3) = X0 )
| ~ in_environment(sk3,X0) ),
inference(superposition,[status(thm)],[c_322,c_72]) ).
tcf(c_2213,plain,
! [X0: $i] :
( greater_or_equal(X0,sk1(sk3))
| greater(sk1(sk3),X0)
| ( sk1(sk3) = X0 )
| ~ in_environment(sk3,X0) ),
inference(superposition,[status(thm)],[c_2141,c_74]) ).
tcf(c_2216,plain,
! [X0: $i,X1: $i] :
( greater(X0,sk1(sk3))
| greater(sk1(sk3),X1)
| ( sk1(sk3) = X0 )
| ~ in_environment(sk3,X0)
| ~ greater(X0,X1) ),
inference(superposition,[status(thm)],[c_2141,c_71]) ).
tcf(c_2217,plain,
! [X0: $i] :
( greater_or_equal(sk1(sk3),X0)
| greater(X0,sk1(sk3))
| ( sk1(sk3) = X0 )
| ~ in_environment(sk3,X0) ),
inference(superposition,[status(thm)],[c_2141,c_74]) ).
tcf(c_2273,plain,
! [X0: $i,X1: $i] :
( greater(sk4(sk2(sk3)),X1)
| ~ greater(X0,X1)
| ~ greater(sk4(sk2(sk3)),X0) ),
inference(instantiation,[status(thm)],[c_71]) ).
tcf(c_2363,plain,
! [X0: $i] :
( greater(sk4(sk2(sk3)),X0)
| ( equilibrium(sk3) = sk2(sk3) )
| ( sk4(sk2(sk3)) = sk2(sk3) )
| ~ in_environment(sk3,sk2(sk3))
| ~ greater(equilibrium(sk3),X0) ),
inference(superposition,[status(thm)],[c_2091,c_2065]) ).
tcf(c_2394,plain,
! [X0: $i,X1: $i] :
( ( X1 = growth_rate(first_movers,sk4(sk2(sk3))) )
| ( X1 != X0 )
| ( growth_rate(first_movers,sk4(sk2(sk3))) != X0 ) ),
inference(instantiation,[status(thm)],[c_1618]) ).
tcf(c_2395,plain,
( ( zero = growth_rate(first_movers,sk4(sk2(sk3))) )
| ( zero != zero )
| ( growth_rate(first_movers,sk4(sk2(sk3))) != zero ) ),
inference(instantiation,[status(thm)],[c_2394]) ).
tcf(c_2438,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(X0,X2)
| ~ greater(X1,X2)
| ( X0 != X1 ) ),
inference(resolution,[status(thm)],[c_1619,c_1616]) ).
tcf(c_2472,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(growth_rate(first_movers,sk4(sk1(sk3))),X1)
| ~ greater(X0,X2)
| ( X1 != X2 )
| ( growth_rate(first_movers,sk4(sk1(sk3))) != X0 ) ),
inference(instantiation,[status(thm)],[c_1619]) ).
tcf(c_2474,plain,
( greater(growth_rate(first_movers,sk4(sk1(sk3))),zero)
| ~ greater(zero,zero)
| ( zero != zero )
| ( growth_rate(first_movers,sk4(sk1(sk3))) != zero ) ),
inference(instantiation,[status(thm)],[c_2472]) ).
tcf(c_2486,plain,
! [X0: $i,X1: $i] :
( ( X1 = growth_rate(first_movers,sk4(sk1(sk3))) )
| ( X1 != X0 )
| ( growth_rate(first_movers,sk4(sk1(sk3))) != X0 ) ),
inference(instantiation,[status(thm)],[c_1618]) ).
tcf(c_2487,plain,
( ( zero = growth_rate(first_movers,sk4(sk1(sk3))) )
| ( zero != zero )
| ( growth_rate(first_movers,sk4(sk1(sk3))) != zero ) ),
inference(instantiation,[status(thm)],[c_2486]) ).
tcf(c_2524,plain,
( greater(sk2(sk3),equilibrium(sk3))
| ( equilibrium(sk3) = sk2(sk3) ) ),
inference(superposition,[status(thm)],[c_293,c_73]) ).
tcf(c_2526,plain,
! [X0: $i] :
( greater(X0,sk1(sk3))
| greater(sk1(sk3),X0)
| ( sk1(sk3) = X0 )
| ~ in_environment(sk3,X0) ),
inference(superposition,[status(thm)],[c_2213,c_73]) ).
tcf(c_2626,plain,
! [X0: $i] :
( ( sk1(X0) = sk1(sk3) )
| ( X0 != sk3 ) ),
inference(instantiation,[status(thm)],[c_1624]) ).
tcf(c_2687,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(X2,X1)
| greater(X2,X0)
| ~ greater_or_equal(X2,X0)
| ~ greater(X0,X1) ),
inference(resolution,[status(thm)],[c_2438,c_73]) ).
tcf(c_2689,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(first_movers,sk4(X0)),zero)
| greater(growth_rate(first_movers,sk4(X0)),X1)
| ~ in_environment(sk3,X0)
| ~ greater(zero,X1)
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(resolution,[status(thm)],[c_2438,c_539]) ).
tcf(c_2727,plain,
! [X0: $i] :
( greater_or_equal(sk4(sk2(sk3)),equilibrium(sk3))
| ~ greater_or_equal(sk2(sk3),X0)
| ( equilibrium(sk3) != X0 )
| ( sk4(sk2(sk3)) != sk2(sk3) ) ),
inference(instantiation,[status(thm)],[c_1933]) ).
tcf(c_2728,plain,
! [X0: $i] :
( greater_or_equal(sk4(sk2(sk3)),sk1(sk3))
| ~ greater_or_equal(sk2(sk3),X0)
| ( sk1(sk3) != X0 )
| ( sk4(sk2(sk3)) != sk2(sk3) ) ),
inference(instantiation,[status(thm)],[c_1930]) ).
tcf(c_2758,plain,
( greater(sk2(sk3),sk1(sk3))
| greater(sk1(sk3),equilibrium(sk3))
| ( sk1(sk3) = sk2(sk3) )
| ( equilibrium(sk3) = sk2(sk3) )
| ~ in_environment(sk3,sk2(sk3)) ),
inference(superposition,[status(thm)],[c_2524,c_2216]) ).
tcf(c_2773,plain,
! [X0: $i] :
( ( zero = growth_rate(efficient_producers,sk4(sk1(sk3))) )
| ( zero != X0 )
| ( growth_rate(efficient_producers,sk4(sk1(sk3))) != X0 ) ),
inference(instantiation,[status(thm)],[c_1618]) ).
tcf(c_2774,plain,
( ( zero = growth_rate(efficient_producers,sk4(sk1(sk3))) )
| ( zero != zero )
| ( growth_rate(efficient_producers,sk4(sk1(sk3))) != zero ) ),
inference(instantiation,[status(thm)],[c_2773]) ).
tcf(c_2806,plain,
! [X0: $i] :
( greater(sk4(sk2(sk3)),X0)
| ~ greater(sk2(sk3),X0)
| ~ greater(sk4(sk2(sk3)),sk2(sk3)) ),
inference(instantiation,[status(thm)],[c_2273]) ).
tcf(c_2811,plain,
! [X0: $i,X1: $i] :
( greater(X0,X1)
| ~ greater(growth_rate(efficient_producers,sk4(sk1(sk3))),growth_rate(first_movers,sk4(sk1(sk3))))
| ( X1 != growth_rate(first_movers,sk4(sk1(sk3))) )
| ( X0 != growth_rate(efficient_producers,sk4(sk1(sk3))) ) ),
inference(instantiation,[status(thm)],[c_1619]) ).
tcf(c_2812,plain,
( greater(zero,zero)
| ~ greater(growth_rate(efficient_producers,sk4(sk1(sk3))),growth_rate(first_movers,sk4(sk1(sk3))))
| ( zero != growth_rate(efficient_producers,sk4(sk1(sk3))) )
| ( zero != growth_rate(first_movers,sk4(sk1(sk3))) ) ),
inference(instantiation,[status(thm)],[c_2811]) ).
tcf(c_2858,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(first_movers,sk4(X0)),X1)
| ~ in_environment(sk3,X0)
| ~ greater(zero,X1)
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2689,c_71]) ).
tcf(c_2895,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(X2,X1)
| ~ greater_or_equal(X2,X0)
| ~ greater(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2687,c_71]) ).
tcf(c_2906,plain,
! [X0: $i,X1: $i] :
( greater(sk4(X0),X1)
| ~ in_environment(sk3,X0)
| ~ greater(X0,X1) ),
inference(resolution,[status(thm)],[c_2895,c_91]) ).
tcf(c_2909,plain,
! [X0: $i] :
( greater(sk2(sk3),X0)
| ~ greater(equilibrium(sk3),X0) ),
inference(resolution,[status(thm)],[c_2895,c_293]) ).
tcf(c_2937,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(first_movers,sk4(X0)),X1)
| ~ greater_or_equal(sk4(X0),equilibrium(sk3))
| ~ greater(zero,X1)
| ~ in_environment(sk3,X0) ),
inference(global_subsumption_just,[status(thm)],[c_1990,c_2858]) ).
tcf(c_2938,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(first_movers,sk4(X0)),X1)
| ~ in_environment(sk3,X0)
| ~ greater(zero,X1)
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(renaming,[status(thm)],[c_2937]) ).
tcf(c_2943,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,sk4(X0)),X1)
| ~ in_environment(sk3,X0)
| ~ greater(zero,X1)
| ~ greater_or_equal(sk4(X0),sk1(sk3))
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(superposition,[status(thm)],[c_2938,c_1992]) ).
tcf(c_2973,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,sk4(X0)))
| ( growth_rate(first_movers,sk4(X0)) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(sk4(X0),sk1(sk3))
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(superposition,[status(thm)],[c_662,c_1991]) ).
tcf(c_3044,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,sk4(X0)))
| ( growth_rate(efficient_producers,sk4(X0)) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(sk4(X0),sk1(sk3))
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(superposition,[status(thm)],[c_662,c_2057]) ).
tcf(c_3060,plain,
! [X0: $i] :
( greater(X0,sk1(sk3))
| greater(sk1(sk3),X0)
| greater(sk1(sk3),sk1(sk3))
| ( sk1(sk3) = X0 )
| ~ in_environment(sk3,X0) ),
inference(superposition,[status(thm)],[c_2526,c_2216]) ).
tcf(c_3289,plain,
! [X0: $i] :
( greater(sk4(sk2(sk3)),X0)
| ~ greater(equilibrium(sk3),X0)
| ( sk4(sk2(sk3)) = sk2(sk3) ) ),
inference(global_subsumption_just,[status(thm)],[c_2363,c_88,c_299,c_1904,c_2056,c_2806,c_2909]) ).
tcf(c_3290,plain,
! [X0: $i] :
( greater(sk4(sk2(sk3)),X0)
| ( sk4(sk2(sk3)) = sk2(sk3) )
| ~ greater(equilibrium(sk3),X0) ),
inference(renaming,[status(thm)],[c_3289]) ).
tcf(c_3296,plain,
! [X0: $i] :
( greater_or_equal(sk4(sk2(sk3)),X0)
| ( sk4(sk2(sk3)) = sk2(sk3) )
| ~ greater(equilibrium(sk3),X0) ),
inference(superposition,[status(thm)],[c_3290,c_74]) ).
tcf(c_3326,plain,
( ( sk1(sk3) = sk1(sk3) )
| ( sk3 != sk3 ) ),
inference(instantiation,[status(thm)],[c_2626]) ).
tcf(c_3341,plain,
( greater_or_equal(sk4(sk2(sk3)),equilibrium(sk3))
| ~ greater_or_equal(sk2(sk3),equilibrium(sk3))
| ( equilibrium(sk3) != equilibrium(sk3) )
| ( sk4(sk2(sk3)) != sk2(sk3) ) ),
inference(instantiation,[status(thm)],[c_2727]) ).
tcf(c_3342,plain,
! [X0: $i] :
( ~ greater_or_equal(sk4(X0),equilibrium(sk3))
| ~ greater_or_equal(sk4(X0),sk1(sk3))
| ~ in_environment(sk3,X0)
| ( growth_rate(efficient_producers,sk4(X0)) = zero ) ),
inference(global_subsumption_just,[status(thm)],[c_2124,c_92,c_2124,c_3044]) ).
tcf(c_3343,plain,
! [X0: $i] :
( ( growth_rate(efficient_producers,sk4(X0)) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(sk4(X0),sk1(sk3))
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(renaming,[status(thm)],[c_3342]) ).
tcf(c_3345,plain,
( ( growth_rate(efficient_producers,sk4(sk1(sk3))) = zero )
| ~ in_environment(sk3,sk1(sk3))
| ~ greater_or_equal(sk4(sk1(sk3)),equilibrium(sk3)) ),
inference(superposition,[status(thm)],[c_91,c_3343]) ).
tcf(c_3347,plain,
! [X0: $i] :
( ( sk4(X0) = X0 )
| ( growth_rate(efficient_producers,sk4(X0)) = zero )
| ~ in_environment(sk3,X0)
| ~ greater(X0,sk1(sk3))
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(superposition,[status(thm)],[c_2066,c_3343]) ).
tcf(c_3353,plain,
( greater_or_equal(sk4(sk2(sk3)),sk1(sk3))
| ~ greater_or_equal(sk2(sk3),equilibrium(sk3))
| ( sk1(sk3) != equilibrium(sk3) )
| ( sk4(sk2(sk3)) != sk2(sk3) ) ),
inference(instantiation,[status(thm)],[c_2728]) ).
tcf(c_3381,plain,
! [X0: $i] :
( greater(sk4(X0),X0)
| ( sk4(X0) = X0 )
| ~ in_environment(sk3,X0) ),
inference(superposition,[status(thm)],[c_91,c_73]) ).
tcf(c_3395,plain,
! [X0: $i] :
( greater(X0,sk1(sk3))
| greater(sk1(sk3),X0)
| ~ in_environment(sk3,X0)
| ( sk1(sk3) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_3060,c_2141]) ).
tcf(c_3396,plain,
! [X0: $i] :
( greater(X0,sk1(sk3))
| greater(sk1(sk3),X0)
| ( sk1(sk3) = X0 )
| ~ in_environment(sk3,X0) ),
inference(renaming,[status(thm)],[c_3395]) ).
tcf(c_3413,plain,
! [X0: $i,X1: $i] :
( greater(sk4(X0),X1)
| ( sk4(X0) = X0 )
| ~ in_environment(sk3,X0)
| ~ greater(X0,X1) ),
inference(superposition,[status(thm)],[c_3381,c_71]) ).
tcf(c_3432,plain,
! [X0: $i,X1: $i] :
( greater(sk4(X0),X1)
| ~ greater(X0,X1)
| ~ in_environment(sk3,X0) ),
inference(global_subsumption_just,[status(thm)],[c_3413,c_2906]) ).
tcf(c_3433,plain,
! [X0: $i,X1: $i] :
( greater(sk4(X0),X1)
| ~ in_environment(sk3,X0)
| ~ greater(X0,X1) ),
inference(renaming,[status(thm)],[c_3432]) ).
tcf(c_3435,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(sk4(X0),X1)
| ~ in_environment(sk3,X0)
| ~ greater(X0,X1) ),
inference(superposition,[status(thm)],[c_3433,c_74]) ).
tcf(c_3532,plain,
! [X0: $i,X1: $i] :
( greater(X0,X1)
| ~ greater(sk2(sk3),sk1(sk3))
| ( X1 != sk1(sk3) )
| ( X0 != sk2(sk3) ) ),
inference(instantiation,[status(thm)],[c_1619]) ).
tcf(c_3534,plain,
( ( sk4(sk2(sk3)) = sk2(sk3) )
| ( growth_rate(efficient_producers,sk4(sk2(sk3))) = zero )
| ~ in_environment(sk3,sk2(sk3))
| ~ greater(sk2(sk3),sk1(sk3))
| ~ greater_or_equal(sk4(sk2(sk3)),equilibrium(sk3)) ),
inference(instantiation,[status(thm)],[c_3347]) ).
tcf(c_3542,plain,
( greater(zero,growth_rate(first_movers,sk4(sk2(sk3))))
| ( growth_rate(efficient_producers,sk4(sk2(sk3))) = zero )
| ~ in_environment(sk3,sk2(sk3))
| ~ greater_or_equal(sk4(sk2(sk3)),sk1(sk3))
| ~ greater_or_equal(sk4(sk2(sk3)),equilibrium(sk3)) ),
inference(instantiation,[status(thm)],[c_3044]) ).
tcf(c_3544,plain,
( greater(zero,growth_rate(first_movers,sk4(sk2(sk3))))
| ( growth_rate(first_movers,sk4(sk2(sk3))) = zero )
| ~ in_environment(sk3,sk2(sk3))
| ~ greater_or_equal(sk4(sk2(sk3)),sk1(sk3))
| ~ greater_or_equal(sk4(sk2(sk3)),equilibrium(sk3)) ),
inference(instantiation,[status(thm)],[c_2973]) ).
tcf(c_3545,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,sk4(sk2(sk3))),X0)
| ~ greater(zero,X0)
| ~ in_environment(sk3,sk2(sk3))
| ~ greater_or_equal(sk4(sk2(sk3)),sk1(sk3))
| ~ greater_or_equal(sk4(sk2(sk3)),equilibrium(sk3)) ),
inference(instantiation,[status(thm)],[c_2943]) ).
tcf(c_3575,plain,
! [X0: $i] :
( greater(sk1(sk3),X0)
| greater(sk2(sk3),sk1(sk3))
| ( sk1(sk3) = sk2(sk3) )
| ~ in_environment(sk3,sk2(sk3))
| ~ greater(sk2(sk3),X0) ),
inference(instantiation,[status(thm)],[c_2216]) ).
tcf(c_3581,plain,
( greater(growth_rate(efficient_producers,sk4(sk2(sk3))),zero)
| ( growth_rate(first_movers,sk4(sk2(sk3))) = zero )
| ~ in_environment(sk3,sk2(sk3))
| ~ greater_or_equal(sk4(sk2(sk3)),sk1(sk3))
| ~ greater_or_equal(sk4(sk2(sk3)),equilibrium(sk3)) ),
inference(instantiation,[status(thm)],[c_2125]) ).
tcf(c_3582,plain,
( greater(growth_rate(efficient_producers,sk4(sk2(sk3))),zero)
| ( growth_rate(efficient_producers,sk4(sk2(sk3))) = zero )
| ~ in_environment(sk3,sk2(sk3))
| ~ greater_or_equal(sk4(sk2(sk3)),sk1(sk3))
| ~ greater_or_equal(sk4(sk2(sk3)),equilibrium(sk3)) ),
inference(instantiation,[status(thm)],[c_2124]) ).
tcf(c_3586,plain,
! [X0: $i] :
( greater_or_equal(sk4(sk2(sk3)),X0)
| ( sk4(sk2(sk3)) = sk2(sk3) )
| ~ in_environment(sk3,sk2(sk3))
| ~ greater(sk2(sk3),X0) ),
inference(instantiation,[status(thm)],[c_2066]) ).
tcf(c_3625,plain,
( greater(growth_rate(efficient_producers,sk4(sk2(sk3))),zero)
| ~ greater(zero,zero)
| ~ in_environment(sk3,sk2(sk3))
| ~ greater_or_equal(sk4(sk2(sk3)),sk1(sk3))
| ~ greater_or_equal(sk4(sk2(sk3)),equilibrium(sk3)) ),
inference(instantiation,[status(thm)],[c_3545]) ).
tcf(c_3627,plain,
! [X0: $i,X1: $i] :
( in_environment(X0,X1)
| ~ in_environment(sk3,sk2(sk3))
| ( X1 != sk2(sk3) )
| ( X0 != sk3 ) ),
inference(instantiation,[status(thm)],[c_1620]) ).
tcf(c_3684,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,sk4(sk1(sk3))),X0)
| ~ in_environment(sk3,sk1(sk3))
| ~ greater_or_equal(sk4(sk1(sk3)),sk1(sk3))
| ~ greater(growth_rate(first_movers,sk4(sk1(sk3))),X0) ),
inference(instantiation,[status(thm)],[c_1992]) ).
tcf(c_3685,plain,
( greater(growth_rate(efficient_producers,sk4(sk1(sk3))),zero)
| ~ in_environment(sk3,sk1(sk3))
| ~ greater_or_equal(sk4(sk1(sk3)),sk1(sk3))
| ~ greater(growth_rate(first_movers,sk4(sk1(sk3))),zero) ),
inference(instantiation,[status(thm)],[c_3684]) ).
tcf(c_3733,plain,
( greater_or_equal(sk1(sk3),equilibrium(sk3))
| greater(equilibrium(sk3),sk1(sk3))
| ( sk1(sk3) = equilibrium(sk3) )
| ~ in_environment(sk3,equilibrium(sk3)) ),
inference(instantiation,[status(thm)],[c_2217]) ).
tcf(c_3814,plain,
! [X0: $i,X1: $i] :
( ( X1 = sk2(sk3) )
| ( X1 != X0 )
| ( sk2(sk3) != X0 ) ),
inference(instantiation,[status(thm)],[c_1618]) ).
tcf(c_3827,plain,
! [X0: $i] :
( greater(X0,sk1(sk3))
| ~ greater(sk2(sk3),sk1(sk3))
| ( X0 != sk2(sk3) )
| ( sk1(sk3) != sk1(sk3) ) ),
inference(instantiation,[status(thm)],[c_3532]) ).
tcf(c_3868,plain,
! [X0: $i] :
( in_environment(sk3,X0)
| ~ in_environment(sk3,sk2(sk3))
| ( sk3 != sk3 )
| ( X0 != sk2(sk3) ) ),
inference(instantiation,[status(thm)],[c_3627]) ).
tcf(c_3993,plain,
! [X0: $i] :
( greater(sk1(sk3),X0)
| ( sk1(sk3) = X0 )
| ~ greater_or_equal(sk1(sk3),X0) ),
inference(instantiation,[status(thm)],[c_73]) ).
tcf(c_3996,plain,
! [X0: $i,X1: $i] :
( ( sk1(sk3) = X1 )
| ( X1 != X0 )
| ( sk1(sk3) != X0 ) ),
inference(instantiation,[status(thm)],[c_1618]) ).
tcf(c_4178,plain,
! [X0: $i,X1: $i] :
( greater(X0,X1)
| ~ greater(growth_rate(efficient_producers,sk4(sk2(sk3))),growth_rate(first_movers,sk4(sk2(sk3))))
| ( X1 != growth_rate(first_movers,sk4(sk2(sk3))) )
| ( X0 != growth_rate(efficient_producers,sk4(sk2(sk3))) ) ),
inference(instantiation,[status(thm)],[c_1619]) ).
tcf(c_4179,plain,
( greater(zero,zero)
| ~ greater(growth_rate(efficient_producers,sk4(sk2(sk3))),growth_rate(first_movers,sk4(sk2(sk3))))
| ( zero != growth_rate(efficient_producers,sk4(sk2(sk3))) )
| ( zero != growth_rate(first_movers,sk4(sk2(sk3))) ) ),
inference(instantiation,[status(thm)],[c_4178]) ).
tcf(c_4234,plain,
! [X0: $i] :
( greater(sk2(sk3),X0)
| ~ greater(equilibrium(sk3),X0) ),
inference(global_subsumption_just,[status(thm)],[c_2018,c_2909]) ).
tcf(c_4236,plain,
( greater(sk2(sk3),sk1(sk3))
| greater(sk1(sk3),equilibrium(sk3))
| ( equilibrium(sk3) = sk1(sk3) )
| ~ in_environment(sk3,equilibrium(sk3)) ),
inference(superposition,[status(thm)],[c_3396,c_4234]) ).
tcf(c_4276,plain,
( greater_or_equal(sk4(sk2(sk3)),equilibrium(sk3))
| ( sk4(sk2(sk3)) = sk2(sk3) )
| ~ in_environment(sk3,sk2(sk3))
| ~ greater(sk2(sk3),equilibrium(sk3)) ),
inference(instantiation,[status(thm)],[c_3586]) ).
tcf(c_4277,plain,
( greater_or_equal(sk4(sk2(sk3)),sk1(sk3))
| ( sk4(sk2(sk3)) = sk2(sk3) )
| ~ in_environment(sk3,sk2(sk3))
| ~ greater(sk2(sk3),sk1(sk3)) ),
inference(instantiation,[status(thm)],[c_3586]) ).
tcf(c_4328,plain,
! [X0: $i] :
( ( X0 = sk2(sk3) )
| ( X0 != equilibrium(sk3) )
| ( sk2(sk3) != equilibrium(sk3) ) ),
inference(instantiation,[status(thm)],[c_3814]) ).
tcf(c_4534,plain,
( in_environment(sk3,equilibrium(sk3))
| ~ in_environment(sk3,sk2(sk3))
| ( sk3 != sk3 )
| ( equilibrium(sk3) != sk2(sk3) ) ),
inference(instantiation,[status(thm)],[c_3868]) ).
tcf(c_4693,plain,
( greater(sk2(sk3),sk1(sk3))
| greater(sk1(sk3),equilibrium(sk3))
| ( sk1(sk3) = sk2(sk3) )
| ( equilibrium(sk3) = sk2(sk3) ) ),
inference(global_subsumption_just,[status(thm)],[c_2758,c_88,c_299,c_2758]) ).
tcf(c_4784,plain,
equilibrium(sk3) = equilibrium(sk3),
inference(instantiation,[status(thm)],[c_1616]) ).
tcf(c_4830,plain,
( greater(sk1(sk3),equilibrium(sk3))
| ( sk1(sk3) = equilibrium(sk3) )
| ~ greater_or_equal(sk1(sk3),equilibrium(sk3)) ),
inference(instantiation,[status(thm)],[c_3993]) ).
tcf(c_4849,plain,
! [X0: $i] :
( ( sk1(sk3) = X0 )
| ( X0 != sk1(sk3) )
| ( sk1(sk3) != sk1(sk3) ) ),
inference(instantiation,[status(thm)],[c_3996]) ).
tcf(c_5145,plain,
( greater_or_equal(sk4(sk2(sk3)),sk1(sk3))
| ( sk4(sk2(sk3)) = sk2(sk3) )
| ~ greater(equilibrium(sk3),sk1(sk3)) ),
inference(instantiation,[status(thm)],[c_3296]) ).
tcf(c_5562,plain,
! [X0: $i,X1: $i] :
( ( X1 = growth_rate(efficient_producers,sk4(sk2(sk3))) )
| ( X1 != X0 )
| ( growth_rate(efficient_producers,sk4(sk2(sk3))) != X0 ) ),
inference(instantiation,[status(thm)],[c_1618]) ).
tcf(c_5563,plain,
( ( zero = growth_rate(efficient_producers,sk4(sk2(sk3))) )
| ( zero != zero )
| ( growth_rate(efficient_producers,sk4(sk2(sk3))) != zero ) ),
inference(instantiation,[status(thm)],[c_5562]) ).
tcf(c_5584,plain,
! [X0: $i] :
( ~ greater_or_equal(sk4(X0),equilibrium(sk3))
| ~ greater_or_equal(sk4(X0),sk1(sk3))
| ~ in_environment(sk3,X0)
| ( growth_rate(first_movers,sk4(X0)) = zero ) ),
inference(global_subsumption_just,[status(thm)],[c_2125,c_92,c_2125,c_2973]) ).
tcf(c_5585,plain,
! [X0: $i] :
( ( growth_rate(first_movers,sk4(X0)) = zero )
| ~ in_environment(sk3,X0)
| ~ greater_or_equal(sk4(X0),sk1(sk3))
| ~ greater_or_equal(sk4(X0),equilibrium(sk3)) ),
inference(renaming,[status(thm)],[c_5584]) ).
tcf(c_5587,plain,
( ( growth_rate(first_movers,sk4(sk1(sk3))) = zero )
| ~ in_environment(sk3,sk1(sk3))
| ~ greater_or_equal(sk4(sk1(sk3)),equilibrium(sk3)) ),
inference(superposition,[status(thm)],[c_91,c_5585]) ).
tcf(c_5615,plain,
~ greater_or_equal(sk4(sk1(sk3)),equilibrium(sk3)),
inference(global_subsumption_just,[status(thm)],[c_5587,c_88,c_321,c_1630,c_1913,c_1912,c_1907,c_1955,c_2474,c_2487,c_2774,c_2812,c_3345,c_3685,c_5587]) ).
tcf(c_5617,plain,
( ~ in_environment(sk3,sk1(sk3))
| ~ greater(sk1(sk3),equilibrium(sk3)) ),
inference(superposition,[status(thm)],[c_3435,c_5615]) ).
tcf(c_6818,plain,
sk4(sk2(sk3)) = sk4(sk2(sk3)),
inference(instantiation,[status(thm)],[c_1616]) ).
tcf(c_7082,plain,
( ( sk1(sk3) = sk2(sk3) )
| ( sk2(sk3) != equilibrium(sk3) )
| ( sk1(sk3) != equilibrium(sk3) ) ),
inference(instantiation,[status(thm)],[c_4328]) ).
tcf(c_7137,plain,
( greater(sk4(sk2(sk3)),sk1(sk3))
| ~ greater(sk2(sk3),sk1(sk3))
| ( sk1(sk3) != sk1(sk3) )
| ( sk4(sk2(sk3)) != sk2(sk3) ) ),
inference(instantiation,[status(thm)],[c_3827]) ).
tcf(c_8499,plain,
( greater(sk2(sk3),sk1(sk3))
| greater(sk1(sk3),equilibrium(sk3))
| ( sk1(sk3) = sk2(sk3) )
| ~ in_environment(sk3,sk2(sk3))
| ~ greater(sk2(sk3),equilibrium(sk3)) ),
inference(instantiation,[status(thm)],[c_3575]) ).
tcf(c_9151,plain,
( ( sk1(sk3) = equilibrium(sk3) )
| ( sk1(sk3) != sk1(sk3) )
| ( equilibrium(sk3) != sk1(sk3) ) ),
inference(instantiation,[status(thm)],[c_4849]) ).
tcf(c_9165,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_9151,c_8499,c_7137,c_7082,c_6818,c_5617,c_5563,c_5145,c_4830,c_4784,c_4693,c_4534,c_4277,c_4276,c_4236,c_4179,c_3733,c_3534,c_3542,c_3544,c_3625,c_3581,c_3582,c_3353,c_3341,c_3326,c_2395,c_2075,c_2064,c_2014,c_1958,c_1943,c_1929,c_1898,c_1903,c_1904,c_1630,c_709,c_321,c_299,c_292,c_88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : MGT029-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/0.31 % Computer : n012.cluster.edu
% 0.04/0.31 % Model : x86_64 x86_64
% 0.04/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.31 % Memory : 8046.5625MB
% 0.04/0.31 % OS : Linux 6.8.0-71-generic
% 0.04/0.31 % CPULimit : 300
% 0.04/0.31 % WCLimit : 300
% 0.04/0.31 % DateTime : Thu Sep 24 01:04:35 UTC 2026
% 0.04/0.31 % CPUTime :
% 0.04/0.31 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/0.33 Running first-order theorem proving
% 0.04/0.33 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
% 0.07/0.34
% 0.07/0.34 % ======== iProver multi-core TPTP/SMT =========
% 0.07/0.34
% 0.07/0.34 % Detected problem language: tptp
% 0.07/0.34 % Proving...
% 3.00/0.98 % SZS status Started for theBenchmark.p
% 3.00/0.98 % SZS status Unsatisfiable for theBenchmark.p
% 3.00/0.98
% 3.00/0.98 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.00/0.98
% 3.00/0.98 % ------ iProver source info
% 3.00/0.98
% 3.00/0.98 % git: date: 2026-07-19 20:42:38 +0200
% 3.00/0.98 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.00/0.98 % git: non_committed_changes: false
% 3.00/0.98
% 3.00/0.98 % ------ Parsing...% successful
% 3.00/0.98
% 3.00/0.98
% 3.00/0.98 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.00/0.98
% 3.00/0.98 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 3.00/0.98
% 3.00/0.98 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.00/0.98
% 3.00/0.98 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.00/0.98 % ------ Proving...
% 3.00/0.98 % ------ Problem Properties
% 3.00/0.98
% 3.00/0.98 %
% 3.00/0.98 % clauses 15
% 3.00/0.98 % conjectures 2
% 3.00/0.98 % EPR 5
% 3.00/0.98 % Horn 9
% 3.00/0.98 % unary 4
% 3.00/0.98 % binary 2
% 3.00/0.98 % lits 41
% 3.00/0.98 % lits eq 6
% 3.00/0.98 % fd_pure 0
% 3.00/0.98 % fd_pseudo 0
% 3.00/0.98 % fd_cond 0
% 3.00/0.98 % fd_pseudo_cond 2
% 3.00/0.98 % AC symbols 0
% 3.00/0.98
% 3.00/0.98 % ------ Input Options Time Limit: Unbounded
% 3.00/0.98
% 3.00/0.98
% 3.00/0.98 % ------
% 3.00/0.98 % Current options:
% 3.00/0.98 % ------
% 3.00/0.98
% 3.00/0.98
% 3.00/0.98 %
% 3.00/0.98
% 3.00/0.98 % ------ Proving...
% 3.00/0.98 %
% 3.00/0.98
% 3.00/0.98 % SZS status Unsatisfiable for theBenchmark.p
% 3.00/0.98
% 3.00/0.98 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.00/0.99
%------------------------------------------------------------------------------