%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT024+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 : n003.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 02:12:23 PM UTC 2026
% Result : Theorem 1.32s 1.27s
% Output : CNFRefutation 1.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 106 ( 11 unt; 0 def)
% Number of atoms : 494 ( 109 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 657 ( 269 ~; 328 |; 48 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 135 ( 0 sgn 131 !; 4 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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_occur) ).
fof(f2,axiom,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> greater(number_of_organizations(X0,X1),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_positive_number_of_organizations) ).
fof(f3,axiom,
! [X0,X1] :
( ( greater_or_equal(X1,equilibrium(X0))
& environment(X0) )
=> ~ greater(equilibrium(X0),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_equilibrium) ).
fof(f4,axiom,
! [X0,X1] :
( ( greater(number_of_organizations(X0,X1),zero)
& in_environment(X0,X1)
& environment(X0) )
=> ( ( ~ greater(equilibrium(X0),X1)
=> constant(resources(X0,X1)) )
& ( greater(equilibrium(X0),X1)
=> decreases(resources(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
fof(f5,axiom,
! [X0,X1] :
( ( in_environment(X0,X1)
& environment(X0) )
=> ( ( constant(resources(X0,X1))
=> constant(number_of_organizations(X0,X1)) )
& ( decreases(resources(X0,X1))
=> ~ decreases(number_of_organizations(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a6) ).
fof(f6,axiom,
! [X0,X1] :
( ( constant(number_of_organizations(X0,X1))
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ( ( greater(zero,growth_rate(first_movers,X1))
& greater(growth_rate(efficient_producers,X1),zero) )
| ( greater(zero,growth_rate(efficient_producers,X1))
& greater(growth_rate(first_movers,X1),zero) )
| ( growth_rate(efficient_producers,X1) = zero
& growth_rate(first_movers,X1) = zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l7) ).
fof(f7,conjecture,
! [X0,X1] :
( ( greater_or_equal(X1,equilibrium(X0))
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ( ( greater(zero,growth_rate(first_movers,X1))
& greater(growth_rate(efficient_producers,X1),zero) )
| ( greater(zero,growth_rate(efficient_producers,X1))
& greater(growth_rate(first_movers,X1),zero) )
| ( growth_rate(efficient_producers,X1) = zero
& growth_rate(first_movers,X1) = zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l6) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( ( greater_or_equal(X1,equilibrium(X0))
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ( ( greater(zero,growth_rate(first_movers,X1))
& greater(growth_rate(efficient_producers,X1),zero) )
| ( greater(zero,growth_rate(efficient_producers,X1))
& greater(growth_rate(first_movers,X1),zero) )
| ( growth_rate(efficient_producers,X1) = zero
& growth_rate(first_movers,X1) = zero ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f10,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(number_of_organizations(X0,X1),zero) ),
inference(ennf_transformation,[],[f2]) ).
fof(f12,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(number_of_organizations(X0,X1),zero) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,equilibrium(X0))
| ~ environment(X0)
| ~ greater(equilibrium(X0),X1) ),
inference(ennf_transformation,[],[f3]) ).
fof(f14,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,equilibrium(X0))
| ~ environment(X0)
| ~ greater(equilibrium(X0),X1) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ( ( greater(equilibrium(X0),X1)
| constant(resources(X0,X1)) )
& ( ~ greater(equilibrium(X0),X1)
| decreases(resources(X0,X1)) ) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f16,plain,
! [X0,X1] :
( ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ( ( greater(equilibrium(X0),X1)
| constant(resources(X0,X1)) )
& ( ~ greater(equilibrium(X0),X1)
| decreases(resources(X0,X1)) ) ) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| ( ( ~ constant(resources(X0,X1))
| constant(number_of_organizations(X0,X1)) )
& ( ~ decreases(resources(X0,X1))
| ~ decreases(number_of_organizations(X0,X1)) ) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f18,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| ( ( ~ constant(resources(X0,X1))
| constant(number_of_organizations(X0,X1)) )
& ( ~ decreases(resources(X0,X1))
| ~ decreases(number_of_organizations(X0,X1)) ) ) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ( greater(zero,growth_rate(first_movers,X1))
& greater(growth_rate(efficient_producers,X1),zero) )
| ( greater(zero,growth_rate(efficient_producers,X1))
& greater(growth_rate(first_movers,X1),zero) )
| ( growth_rate(efficient_producers,X1) = zero
& growth_rate(first_movers,X1) = zero ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f20,plain,
! [X0,X1] :
( ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| ( greater(zero,growth_rate(first_movers,X1))
& greater(growth_rate(efficient_producers,X1),zero) )
| ( greater(zero,growth_rate(efficient_producers,X1))
& greater(growth_rate(first_movers,X1),zero) )
| ( growth_rate(efficient_producers,X1) = zero
& growth_rate(first_movers,X1) = zero ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
? [X0,X1] :
( greater_or_equal(X1,equilibrium(X0))
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0)
& ( ~ greater(zero,growth_rate(first_movers,X1))
| ~ greater(growth_rate(efficient_producers,X1),zero) )
& ( ~ greater(zero,growth_rate(efficient_producers,X1))
| ~ greater(growth_rate(first_movers,X1),zero) )
& ( zero != growth_rate(efficient_producers,X1)
| zero != growth_rate(first_movers,X1) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f22,plain,
? [X0,X1] :
( greater_or_equal(X1,equilibrium(X0))
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0)
& ( ~ greater(zero,growth_rate(first_movers,X1))
| ~ greater(growth_rate(efficient_producers,X1),zero) )
& ( ~ greater(zero,growth_rate(efficient_producers,X1))
| ~ greater(growth_rate(first_movers,X1),zero) )
& ( zero != growth_rate(efficient_producers,X1)
| zero != growth_rate(first_movers,X1) ) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
( greater_or_equal(sK1,equilibrium(sK0))
& subpopulations(first_movers,efficient_producers,sK0,sK1)
& environment(sK0)
& ( ~ greater(zero,growth_rate(first_movers,sK1))
| ~ greater(growth_rate(efficient_producers,sK1),zero) )
& ( ~ greater(zero,growth_rate(efficient_producers,sK1))
| ~ greater(growth_rate(first_movers,sK1),zero) )
& ( zero != growth_rate(efficient_producers,sK1)
| zero != growth_rate(first_movers,sK1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(cnf_transformation,[],[f10]) ).
fof(f25,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(number_of_organizations(X0,X1),zero) ),
inference(cnf_transformation,[],[f12]) ).
fof(f26,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,equilibrium(X0))
| ~ environment(X0)
| ~ greater(equilibrium(X0),X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f27,plain,
! [X0,X1] :
( ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(equilibrium(X0),X1)
| constant(resources(X0,X1)) ),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ constant(resources(X0,X1))
| constant(number_of_organizations(X0,X1)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f31,plain,
! [X0,X1] :
( ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(efficient_producers,X1))
| zero = growth_rate(efficient_producers,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f32,plain,
! [X0,X1] :
( ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(growth_rate(efficient_producers,X1),zero)
| greater(zero,growth_rate(efficient_producers,X1))
| zero = growth_rate(efficient_producers,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f33,plain,
! [X0,X1] :
( ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| zero = growth_rate(efficient_producers,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f34,plain,
! [X0,X1] :
( ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| zero = growth_rate(efficient_producers,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f35,plain,
! [X0,X1] :
( ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(efficient_producers,X1))
| zero = growth_rate(first_movers,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
! [X0,X1] :
( ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(growth_rate(efficient_producers,X1),zero)
| greater(zero,growth_rate(efficient_producers,X1))
| zero = growth_rate(first_movers,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f37,plain,
! [X0,X1] :
( ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| zero = growth_rate(first_movers,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X0,X1] :
( ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| zero = growth_rate(first_movers,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
greater_or_equal(sK1,equilibrium(sK0)),
inference(cnf_transformation,[],[f23]) ).
fof(f40,plain,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f23]) ).
fof(f41,plain,
environment(sK0),
inference(cnf_transformation,[],[f23]) ).
fof(f42,plain,
( ~ greater(zero,growth_rate(first_movers,sK1))
| ~ greater(growth_rate(efficient_producers,sK1),zero) ),
inference(cnf_transformation,[],[f23]) ).
fof(f43,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK1))
| ~ greater(growth_rate(first_movers,sK1),zero) ),
inference(cnf_transformation,[],[f23]) ).
fof(f44,plain,
( zero != growth_rate(efficient_producers,sK1)
| zero != growth_rate(first_movers,sK1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( greater(number_of_organizations(X0,X1),zero)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( ~ environment(X0)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ greater(equilibrium(X0),X1) ),
inference(cnf_transformation,[],[f26]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( constant(resources(X0,X1))
| greater(equilibrium(X0),X1)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(number_of_organizations(X0,X1),zero) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ constant(resources(X0,X1)) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_56,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)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_57,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)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_58,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)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_59,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)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_60,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)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_61,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)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_62,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)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_63,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)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_64,negated_conjecture,
( ( growth_rate(efficient_producers,sK1) != zero )
| ( growth_rate(first_movers,sK1) != zero ) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_65,negated_conjecture,
( ~ greater(zero,growth_rate(efficient_producers,sK1))
| ~ greater(growth_rate(first_movers,sK1),zero) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_66,negated_conjecture,
( ~ greater(zero,growth_rate(first_movers,sK1))
| ~ greater(growth_rate(efficient_producers,sK1),zero) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_67,negated_conjecture,
environment(sK0),
inference(cnf_transformation,[],[f41]) ).
tcf(c_68,negated_conjecture,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f40]) ).
tcf(c_69,negated_conjecture,
greater_or_equal(sK1,equilibrium(sK0)),
inference(cnf_transformation,[],[f39]) ).
tcf(c_424,plain,
! [X0: $i,X1: $i] :
( ~ environment(X0)
| ~ greater(equilibrium(X0),X1)
| ( X1 != sK1 )
| ( equilibrium(X0) != equilibrium(sK0) ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_69]) ).
tcf(c_425,plain,
! [X0: $i] :
( ~ environment(X0)
| ~ greater(equilibrium(X0),sK1)
| ( equilibrium(X0) != equilibrium(sK0) ) ),
inference(unflattening,[status(thm)],[c_424]) ).
tcf(c_439,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( constant(number_of_organizations(X1,X3))
| ~ environment(X1)
| ~ environment(X0)
| ~ constant(resources(X1,X3))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_55]) ).
tcf(c_440,plain,
! [X0: $i,X1: $i] :
( constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| ~ constant(resources(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(unflattening,[status(thm)],[c_439]) ).
tcf(c_469,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( constant(resources(X1,X3))
| greater(equilibrium(X1),X3)
| ~ environment(X1)
| ~ environment(X0)
| ~ greater(number_of_organizations(X1,X3),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_53]) ).
tcf(c_470,plain,
! [X0: $i,X1: $i] :
( constant(resources(X0,X1))
| greater(equilibrium(X0),X1)
| ~ environment(X0)
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(unflattening,[status(thm)],[c_469]) ).
tcf(c_472,plain,
! [X0: $i,X1: $i] :
( constant(resources(X0,X1))
| greater(equilibrium(X0),X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_470,c_50,c_470]) ).
tcf(c_531,plain,
! [X0: $i,X1: $i] :
( constant(resources(X0,X1))
| greater(equilibrium(X0),X1)
| ~ environment(X0)
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_472,c_68]) ).
tcf(c_532,plain,
( constant(resources(sK0,sK1))
| greater(equilibrium(sK0),sK1)
| ~ environment(sK0) ),
inference(unflattening,[status(thm)],[c_531]) ).
tcf(c_533,plain,
( constant(resources(sK0,sK1))
| greater(equilibrium(sK0),sK1) ),
inference(global_subsumption_just,[status(thm)],[c_532,c_67,c_532]) ).
tcf(c_551,plain,
! [X0: $i,X1: $i] :
( constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| ~ constant(resources(X0,X1))
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_440,c_68]) ).
tcf(c_552,plain,
( constant(number_of_organizations(sK0,sK1))
| ~ environment(sK0)
| ~ constant(resources(sK0,sK1)) ),
inference(unflattening,[status(thm)],[c_551]) ).
tcf(c_553,plain,
( constant(number_of_organizations(sK0,sK1))
| ~ constant(resources(sK0,sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_552,c_67,c_552]) ).
tcf(c_561,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)
| ~ constant(number_of_organizations(X0,X1))
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_63,c_68]) ).
tcf(c_562,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| greater(zero,growth_rate(first_movers,sK1))
| ( growth_rate(efficient_producers,sK1) = zero )
| ~ environment(sK0)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(unflattening,[status(thm)],[c_561]) ).
tcf(c_563,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| greater(zero,growth_rate(first_movers,sK1))
| ( growth_rate(efficient_producers,sK1) = zero )
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_562,c_67,c_562]) ).
tcf(c_577,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)
| ~ constant(number_of_organizations(X0,X1))
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_62,c_68]) ).
tcf(c_578,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| greater(growth_rate(efficient_producers,sK1),zero)
| ( growth_rate(efficient_producers,sK1) = zero )
| ~ environment(sK0)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(unflattening,[status(thm)],[c_577]) ).
tcf(c_579,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| ~ constant(number_of_organizations(sK0,sK1))
| ( growth_rate(efficient_producers,sK1) = zero ) ),
inference(global_subsumption_just,[status(thm)],[c_578,c_67,c_66,c_563,c_578]) ).
tcf(c_580,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| ( growth_rate(efficient_producers,sK1) = zero )
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(renaming,[status(thm)],[c_579]) ).
tcf(c_590,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)
| ~ constant(number_of_organizations(X0,X1))
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_61,c_68]) ).
tcf(c_591,plain,
( greater(zero,growth_rate(first_movers,sK1))
| greater(growth_rate(first_movers,sK1),zero)
| ( growth_rate(efficient_producers,sK1) = zero )
| ~ environment(sK0)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(unflattening,[status(thm)],[c_590]) ).
tcf(c_592,plain,
( greater(zero,growth_rate(first_movers,sK1))
| ~ constant(number_of_organizations(sK0,sK1))
| ( growth_rate(efficient_producers,sK1) = zero ) ),
inference(global_subsumption_just,[status(thm)],[c_591,c_67,c_66,c_65,c_563,c_578,c_591]) ).
tcf(c_593,plain,
( greater(zero,growth_rate(first_movers,sK1))
| ( growth_rate(efficient_producers,sK1) = zero )
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(renaming,[status(thm)],[c_592]) ).
tcf(c_603,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)
| ~ constant(number_of_organizations(X0,X1))
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_60,c_68]) ).
tcf(c_604,plain,
( greater(growth_rate(efficient_producers,sK1),zero)
| greater(growth_rate(first_movers,sK1),zero)
| ( growth_rate(efficient_producers,sK1) = zero )
| ~ environment(sK0)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(unflattening,[status(thm)],[c_603]) ).
tcf(c_605,plain,
( ( growth_rate(efficient_producers,sK1) = zero )
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_604,c_67,c_66,c_65,c_580,c_593,c_604]) ).
tcf(c_613,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)
| ~ constant(number_of_organizations(X0,X1))
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_68]) ).
tcf(c_614,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| greater(zero,growth_rate(first_movers,sK1))
| ( growth_rate(first_movers,sK1) = zero )
| ~ environment(sK0)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(unflattening,[status(thm)],[c_613]) ).
tcf(c_615,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| greater(zero,growth_rate(first_movers,sK1))
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_614,c_67,c_64,c_605,c_614]) ).
tcf(c_626,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)
| ~ constant(number_of_organizations(X0,X1))
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_68]) ).
tcf(c_627,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| greater(growth_rate(efficient_producers,sK1),zero)
| ( growth_rate(first_movers,sK1) = zero )
| ~ environment(sK0)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(unflattening,[status(thm)],[c_626]) ).
tcf(c_628,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_627,c_67,c_66,c_64,c_605,c_615,c_627]) ).
tcf(c_636,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)
| ~ constant(number_of_organizations(X0,X1))
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_57,c_68]) ).
tcf(c_637,plain,
( greater(zero,growth_rate(first_movers,sK1))
| greater(growth_rate(first_movers,sK1),zero)
| ( growth_rate(first_movers,sK1) = zero )
| ~ environment(sK0)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(unflattening,[status(thm)],[c_636]) ).
tcf(c_638,plain,
( greater(zero,growth_rate(first_movers,sK1))
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_637,c_67,c_65,c_64,c_605,c_628,c_637]) ).
tcf(c_646,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)
| ~ constant(number_of_organizations(X0,X1))
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( X1 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_68]) ).
tcf(c_647,plain,
( greater(growth_rate(efficient_producers,sK1),zero)
| greater(growth_rate(first_movers,sK1),zero)
| ( growth_rate(first_movers,sK1) = zero )
| ~ environment(sK0)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(unflattening,[status(thm)],[c_646]) ).
tcf(c_648,plain,
~ constant(number_of_organizations(sK0,sK1)),
inference(global_subsumption_just,[status(thm)],[c_647,c_67,c_66,c_65,c_64,c_605,c_628,c_638,c_647]) ).
tcf(c_671,plain,
! [X0: $i] :
( ~ greater(equilibrium(X0),sK1)
| ( X0 != sK0 )
| ( equilibrium(X0) != equilibrium(sK0) ) ),
inference(resolution_lifted,[status(thm)],[c_425,c_67]) ).
tcf(c_672,plain,
( ~ greater(equilibrium(sK0),sK1)
| ( equilibrium(sK0) != equilibrium(sK0) ) ),
inference(unflattening,[status(thm)],[c_671]) ).
tcf(c_673,plain,
equilibrium(sK0) != equilibrium(sK0),
inference(global_subsumption_just,[status(thm)],[c_672,c_533,c_553,c_648,c_672]) ).
tcf(c_679,plain,
iProver_spec_dis_eq_i(equilibrium(sK0),equilibrium(sK0)),
inference(dis_equality_elim,[status(thm)],[c_673]) ).
tcf(c_681,plain,
! [X0: $i] : ~ iProver_spec_dis_eq_i(X0,X0),
theory(irreflexivity) ).
tcf(c_691,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_679,c_681]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT024+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 01:05:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 1.32/1.27 % SZS status Started for theBenchmark.p
% 1.32/1.27 % SZS status Theorem for theBenchmark.p
% 1.32/1.27
% 1.32/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.32/1.27
% 1.32/1.27 % ------ iProver source info
% 1.32/1.27
% 1.32/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.32/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.32/1.27 % git: non_committed_changes: false
% 1.32/1.27
% 1.32/1.27 % ------ Parsing...
% 1.32/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.32/1.27
% 1.32/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e %
% 1.32/1.27
% 1.32/1.27 % SZS status Theorem for theBenchmark.p
% 1.32/1.27
% 1.32/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.32/1.27
% 1.32/1.27
%------------------------------------------------------------------------------