TSTP Solution File: MGT024+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : MGT024+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 09:14:16 EDT 2023
% Result : Theorem 0.84s 1.13s
% Output : CNFRefutation 0.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 9
% Syntax : Number of formulae : 108 ( 11 unt; 0 def)
% Number of atoms : 512 ( 112 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 686 ( 282 ~; 333 |; 58 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% 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 : 137 ( 0 sgn; 66 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> in_environment(X0,X1) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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) )
| ( zero = growth_rate(efficient_producers,X1)
& zero = growth_rate(first_movers,X1) ) ) ),
file('/export/starexec/sandbox/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) )
| ( zero = growth_rate(efficient_producers,X1)
& zero = growth_rate(first_movers,X1) ) ) ),
file('/export/starexec/sandbox/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) )
| ( zero = growth_rate(efficient_producers,X1)
& zero = growth_rate(first_movers,X1) ) ) ),
inference(negated_conjecture,[],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f10,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( greater(number_of_organizations(X0,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f12,plain,
! [X0,X1] :
( greater(number_of_organizations(X0,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( ~ greater(equilibrium(X0),X1)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ environment(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f14,plain,
! [X0,X1] :
( ~ greater(equilibrium(X0),X1)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ environment(X0) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( ( ( constant(resources(X0,X1))
| greater(equilibrium(X0),X1) )
& ( decreases(resources(X0,X1))
| ~ greater(equilibrium(X0),X1) ) )
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f16,plain,
! [X0,X1] :
( ( ( constant(resources(X0,X1))
| greater(equilibrium(X0),X1) )
& ( decreases(resources(X0,X1))
| ~ greater(equilibrium(X0),X1) ) )
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( ( constant(number_of_organizations(X0,X1))
| ~ constant(resources(X0,X1)) )
& ( ~ decreases(number_of_organizations(X0,X1))
| ~ decreases(resources(X0,X1)) ) )
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f18,plain,
! [X0,X1] :
( ( ( constant(number_of_organizations(X0,X1))
| ~ constant(resources(X0,X1)) )
& ( ~ decreases(number_of_organizations(X0,X1))
| ~ decreases(resources(X0,X1)) ) )
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( ( 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) )
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f20,plain,
! [X0,X1] :
( ( 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) )
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
? [X0,X1] :
( ( ~ 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) )
& greater_or_equal(X1,equilibrium(X0))
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f22,plain,
? [X0,X1] :
( ( ~ 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) )
& greater_or_equal(X1,equilibrium(X0))
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
( ? [X0,X1] :
( ( ~ 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) )
& greater_or_equal(X1,equilibrium(X0))
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ( ( ~ 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) )
& greater_or_equal(sK1,equilibrium(sK0))
& subpopulations(first_movers,efficient_producers,sK0,sK1)
& environment(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f24,plain,
( ( ~ 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) )
& greater_or_equal(sK1,equilibrium(sK0))
& subpopulations(first_movers,efficient_producers,sK0,sK1)
& environment(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f22,f23]) ).
fof(f25,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f10]) ).
fof(f26,plain,
! [X0,X1] :
( greater(number_of_organizations(X0,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f27,plain,
! [X0,X1] :
( ~ greater(equilibrium(X0),X1)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f29,plain,
! [X0,X1] :
( constant(resources(X0,X1))
| greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f16]) ).
fof(f31,plain,
! [X0,X1] :
( constant(number_of_organizations(X0,X1))
| ~ constant(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f18]) ).
fof(f32,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| zero = growth_rate(first_movers,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f33,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| zero = growth_rate(efficient_producers,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f34,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(zero,growth_rate(efficient_producers,X1))
| zero = growth_rate(first_movers,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f35,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(zero,growth_rate(efficient_producers,X1))
| zero = growth_rate(efficient_producers,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f36,plain,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| zero = growth_rate(first_movers,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f37,plain,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| zero = growth_rate(efficient_producers,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(efficient_producers,X1))
| zero = growth_rate(first_movers,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(efficient_producers,X1))
| zero = growth_rate(efficient_producers,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f20]) ).
fof(f40,plain,
environment(sK0),
inference(cnf_transformation,[],[f24]) ).
fof(f41,plain,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f42,plain,
greater_or_equal(sK1,equilibrium(sK0)),
inference(cnf_transformation,[],[f24]) ).
fof(f43,plain,
( zero != growth_rate(efficient_producers,sK1)
| zero != growth_rate(first_movers,sK1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f44,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK1))
| ~ greater(growth_rate(first_movers,sK1),zero) ),
inference(cnf_transformation,[],[f24]) ).
fof(f45,plain,
( ~ greater(zero,growth_rate(first_movers,sK1))
| ~ greater(growth_rate(efficient_producers,sK1),zero) ),
inference(cnf_transformation,[],[f24]) ).
cnf(c_49,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(cnf_transformation,[],[f25]) ).
cnf(c_50,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(number_of_organizations(X0,X1),zero) ),
inference(cnf_transformation,[],[f26]) ).
cnf(c_51,plain,
( ~ greater(equilibrium(X0),X1)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f27]) ).
cnf(c_52,plain,
( ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(equilibrium(X0),X1)
| constant(resources(X0,X1)) ),
inference(cnf_transformation,[],[f29]) ).
cnf(c_54,plain,
( ~ constant(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| constant(number_of_organizations(X0,X1)) ),
inference(cnf_transformation,[],[f31]) ).
cnf(c_56,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| growth_rate(efficient_producers,X1) = zero
| greater(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(efficient_producers,X1)) ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_57,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| growth_rate(first_movers,X1) = zero
| greater(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(efficient_producers,X1)) ),
inference(cnf_transformation,[],[f38]) ).
cnf(c_58,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| growth_rate(efficient_producers,X1) = zero
| greater(growth_rate(first_movers,X1),zero)
| greater(zero,growth_rate(first_movers,X1)) ),
inference(cnf_transformation,[],[f37]) ).
cnf(c_59,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| growth_rate(first_movers,X1) = zero
| greater(growth_rate(first_movers,X1),zero)
| greater(zero,growth_rate(first_movers,X1)) ),
inference(cnf_transformation,[],[f36]) ).
cnf(c_60,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| growth_rate(efficient_producers,X1) = zero
| greater(growth_rate(efficient_producers,X1),zero)
| greater(zero,growth_rate(efficient_producers,X1)) ),
inference(cnf_transformation,[],[f35]) ).
cnf(c_61,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| growth_rate(first_movers,X1) = zero
| greater(growth_rate(efficient_producers,X1),zero)
| greater(zero,growth_rate(efficient_producers,X1)) ),
inference(cnf_transformation,[],[f34]) ).
cnf(c_62,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| growth_rate(efficient_producers,X1) = zero
| greater(growth_rate(first_movers,X1),zero)
| greater(growth_rate(efficient_producers,X1),zero) ),
inference(cnf_transformation,[],[f33]) ).
cnf(c_63,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| growth_rate(first_movers,X1) = zero
| greater(growth_rate(first_movers,X1),zero)
| greater(growth_rate(efficient_producers,X1),zero) ),
inference(cnf_transformation,[],[f32]) ).
cnf(c_64,negated_conjecture,
( ~ greater(growth_rate(efficient_producers,sK1),zero)
| ~ greater(zero,growth_rate(first_movers,sK1)) ),
inference(cnf_transformation,[],[f45]) ).
cnf(c_65,negated_conjecture,
( ~ greater(growth_rate(first_movers,sK1),zero)
| ~ greater(zero,growth_rate(efficient_producers,sK1)) ),
inference(cnf_transformation,[],[f44]) ).
cnf(c_66,negated_conjecture,
( growth_rate(first_movers,sK1) != zero
| growth_rate(efficient_producers,sK1) != zero ),
inference(cnf_transformation,[],[f43]) ).
cnf(c_67,negated_conjecture,
greater_or_equal(sK1,equilibrium(sK0)),
inference(cnf_transformation,[],[f42]) ).
cnf(c_68,negated_conjecture,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f41]) ).
cnf(c_69,negated_conjecture,
environment(sK0),
inference(cnf_transformation,[],[f40]) ).
cnf(c_424,plain,
( equilibrium(X0) != equilibrium(sK0)
| X1 != sK1
| ~ greater(equilibrium(X0),X1)
| ~ environment(X0) ),
inference(resolution_lifted,[status(thm)],[c_51,c_67]) ).
cnf(c_425,plain,
( equilibrium(X0) != equilibrium(sK0)
| ~ greater(equilibrium(X0),sK1)
| ~ environment(X0) ),
inference(unflattening,[status(thm)],[c_424]) ).
cnf(c_454,plain,
( X0 != X1
| X2 != X3
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ constant(resources(X1,X3))
| ~ environment(X0)
| ~ environment(X1)
| constant(number_of_organizations(X1,X3)) ),
inference(resolution_lifted,[status(thm)],[c_49,c_54]) ).
cnf(c_455,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(resources(X0,X1))
| ~ environment(X0)
| constant(number_of_organizations(X0,X1)) ),
inference(unflattening,[status(thm)],[c_454]) ).
cnf(c_487,plain,
( X0 != X1
| X2 != X3
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(number_of_organizations(X1,X3),zero)
| ~ environment(X0)
| ~ environment(X1)
| greater(equilibrium(X1),X3)
| constant(resources(X1,X3)) ),
inference(resolution_lifted,[status(thm)],[c_49,c_52]) ).
cnf(c_488,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ environment(X0)
| greater(equilibrium(X0),X1)
| constant(resources(X0,X1)) ),
inference(unflattening,[status(thm)],[c_487]) ).
cnf(c_490,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(equilibrium(X0),X1)
| constant(resources(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_488,c_50,c_488]) ).
cnf(c_521,plain,
( X0 != sK0
| X1 != sK1
| first_movers != first_movers
| efficient_producers != efficient_producers
| ~ environment(X0)
| greater(equilibrium(X0),X1)
| constant(resources(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_490,c_68]) ).
cnf(c_522,plain,
( ~ environment(sK0)
| greater(equilibrium(sK0),sK1)
| constant(resources(sK0,sK1)) ),
inference(unflattening,[status(thm)],[c_521]) ).
cnf(c_523,plain,
( greater(equilibrium(sK0),sK1)
| constant(resources(sK0,sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_522,c_69,c_522]) ).
cnf(c_541,plain,
( X0 != sK0
| X1 != sK1
| first_movers != first_movers
| efficient_producers != efficient_producers
| ~ constant(resources(X0,X1))
| ~ environment(X0)
| constant(number_of_organizations(X0,X1)) ),
inference(resolution_lifted,[status(thm)],[c_455,c_68]) ).
cnf(c_542,plain,
( ~ constant(resources(sK0,sK1))
| ~ environment(sK0)
| constant(number_of_organizations(sK0,sK1)) ),
inference(unflattening,[status(thm)],[c_541]) ).
cnf(c_543,plain,
( ~ constant(resources(sK0,sK1))
| constant(number_of_organizations(sK0,sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_542,c_69,c_542]) ).
cnf(c_561,plain,
( X0 != sK0
| X1 != sK1
| first_movers != first_movers
| efficient_producers != efficient_producers
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| growth_rate(first_movers,X1) = zero
| greater(growth_rate(first_movers,X1),zero)
| greater(growth_rate(efficient_producers,X1),zero) ),
inference(resolution_lifted,[status(thm)],[c_63,c_68]) ).
cnf(c_562,plain,
( ~ constant(number_of_organizations(sK0,sK1))
| ~ environment(sK0)
| growth_rate(first_movers,sK1) = zero
| greater(growth_rate(first_movers,sK1),zero)
| greater(growth_rate(efficient_producers,sK1),zero) ),
inference(unflattening,[status(thm)],[c_561]) ).
cnf(c_577,plain,
( X0 != sK0
| X1 != sK1
| first_movers != first_movers
| efficient_producers != efficient_producers
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| growth_rate(efficient_producers,X1) = zero
| greater(growth_rate(first_movers,X1),zero)
| greater(growth_rate(efficient_producers,X1),zero) ),
inference(resolution_lifted,[status(thm)],[c_62,c_68]) ).
cnf(c_578,plain,
( ~ constant(number_of_organizations(sK0,sK1))
| ~ environment(sK0)
| growth_rate(efficient_producers,sK1) = zero
| greater(growth_rate(first_movers,sK1),zero)
| greater(growth_rate(efficient_producers,sK1),zero) ),
inference(unflattening,[status(thm)],[c_577]) ).
cnf(c_579,plain,
( ~ constant(number_of_organizations(sK0,sK1))
| greater(growth_rate(first_movers,sK1),zero)
| greater(growth_rate(efficient_producers,sK1),zero) ),
inference(global_subsumption_just,[status(thm)],[c_578,c_69,c_66,c_562,c_578]) ).
cnf(c_590,plain,
( X0 != sK0
| X1 != sK1
| first_movers != first_movers
| efficient_producers != efficient_producers
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| growth_rate(first_movers,X1) = zero
| greater(growth_rate(efficient_producers,X1),zero)
| greater(zero,growth_rate(efficient_producers,X1)) ),
inference(resolution_lifted,[status(thm)],[c_61,c_68]) ).
cnf(c_591,plain,
( ~ constant(number_of_organizations(sK0,sK1))
| ~ environment(sK0)
| growth_rate(first_movers,sK1) = zero
| greater(growth_rate(efficient_producers,sK1),zero)
| greater(zero,growth_rate(efficient_producers,sK1)) ),
inference(unflattening,[status(thm)],[c_590]) ).
cnf(c_592,plain,
( greater(growth_rate(efficient_producers,sK1),zero)
| growth_rate(first_movers,sK1) = zero
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_591,c_69,c_65,c_579,c_591]) ).
cnf(c_593,plain,
( ~ constant(number_of_organizations(sK0,sK1))
| growth_rate(first_movers,sK1) = zero
| greater(growth_rate(efficient_producers,sK1),zero) ),
inference(renaming,[status(thm)],[c_592]) ).
cnf(c_603,plain,
( X0 != sK0
| X1 != sK1
| first_movers != first_movers
| efficient_producers != efficient_producers
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| growth_rate(efficient_producers,X1) = zero
| greater(growth_rate(efficient_producers,X1),zero)
| greater(zero,growth_rate(efficient_producers,X1)) ),
inference(resolution_lifted,[status(thm)],[c_60,c_68]) ).
cnf(c_604,plain,
( ~ constant(number_of_organizations(sK0,sK1))
| ~ environment(sK0)
| growth_rate(efficient_producers,sK1) = zero
| greater(growth_rate(efficient_producers,sK1),zero)
| greater(zero,growth_rate(efficient_producers,sK1)) ),
inference(unflattening,[status(thm)],[c_603]) ).
cnf(c_605,plain,
( greater(growth_rate(efficient_producers,sK1),zero)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_604,c_69,c_65,c_66,c_579,c_593,c_604]) ).
cnf(c_606,plain,
( ~ constant(number_of_organizations(sK0,sK1))
| greater(growth_rate(efficient_producers,sK1),zero) ),
inference(renaming,[status(thm)],[c_605]) ).
cnf(c_613,plain,
( X0 != sK0
| X1 != sK1
| first_movers != first_movers
| efficient_producers != efficient_producers
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| growth_rate(first_movers,X1) = zero
| greater(growth_rate(first_movers,X1),zero)
| greater(zero,growth_rate(first_movers,X1)) ),
inference(resolution_lifted,[status(thm)],[c_59,c_68]) ).
cnf(c_614,plain,
( ~ constant(number_of_organizations(sK0,sK1))
| ~ environment(sK0)
| growth_rate(first_movers,sK1) = zero
| greater(growth_rate(first_movers,sK1),zero)
| greater(zero,growth_rate(first_movers,sK1)) ),
inference(unflattening,[status(thm)],[c_613]) ).
cnf(c_615,plain,
( greater(growth_rate(first_movers,sK1),zero)
| growth_rate(first_movers,sK1) = zero
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_614,c_69,c_64,c_579,c_614]) ).
cnf(c_616,plain,
( ~ constant(number_of_organizations(sK0,sK1))
| growth_rate(first_movers,sK1) = zero
| greater(growth_rate(first_movers,sK1),zero) ),
inference(renaming,[status(thm)],[c_615]) ).
cnf(c_626,plain,
( X0 != sK0
| X1 != sK1
| first_movers != first_movers
| efficient_producers != efficient_producers
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| growth_rate(efficient_producers,X1) = zero
| greater(growth_rate(first_movers,X1),zero)
| greater(zero,growth_rate(first_movers,X1)) ),
inference(resolution_lifted,[status(thm)],[c_58,c_68]) ).
cnf(c_627,plain,
( ~ constant(number_of_organizations(sK0,sK1))
| ~ environment(sK0)
| growth_rate(efficient_producers,sK1) = zero
| greater(growth_rate(first_movers,sK1),zero)
| greater(zero,growth_rate(first_movers,sK1)) ),
inference(unflattening,[status(thm)],[c_626]) ).
cnf(c_628,plain,
( greater(growth_rate(first_movers,sK1),zero)
| ~ constant(number_of_organizations(sK0,sK1)) ),
inference(global_subsumption_just,[status(thm)],[c_627,c_69,c_64,c_66,c_579,c_616,c_627]) ).
cnf(c_629,plain,
( ~ constant(number_of_organizations(sK0,sK1))
| greater(growth_rate(first_movers,sK1),zero) ),
inference(renaming,[status(thm)],[c_628]) ).
cnf(c_636,plain,
( X0 != sK0
| X1 != sK1
| first_movers != first_movers
| efficient_producers != efficient_producers
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| growth_rate(first_movers,X1) = zero
| greater(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(efficient_producers,X1)) ),
inference(resolution_lifted,[status(thm)],[c_57,c_68]) ).
cnf(c_637,plain,
( ~ constant(number_of_organizations(sK0,sK1))
| ~ environment(sK0)
| growth_rate(first_movers,sK1) = zero
| greater(zero,growth_rate(first_movers,sK1))
| greater(zero,growth_rate(efficient_producers,sK1)) ),
inference(unflattening,[status(thm)],[c_636]) ).
cnf(c_638,plain,
( ~ constant(number_of_organizations(sK0,sK1))
| growth_rate(first_movers,sK1) = zero ),
inference(global_subsumption_just,[status(thm)],[c_637,c_69,c_65,c_64,c_606,c_629,c_637]) ).
cnf(c_646,plain,
( X0 != sK0
| X1 != sK1
| first_movers != first_movers
| efficient_producers != efficient_producers
| ~ constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| growth_rate(efficient_producers,X1) = zero
| greater(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(efficient_producers,X1)) ),
inference(resolution_lifted,[status(thm)],[c_56,c_68]) ).
cnf(c_647,plain,
( ~ constant(number_of_organizations(sK0,sK1))
| ~ environment(sK0)
| growth_rate(efficient_producers,sK1) = zero
| greater(zero,growth_rate(first_movers,sK1))
| greater(zero,growth_rate(efficient_producers,sK1)) ),
inference(unflattening,[status(thm)],[c_646]) ).
cnf(c_648,plain,
~ constant(number_of_organizations(sK0,sK1)),
inference(global_subsumption_just,[status(thm)],[c_647,c_69,c_65,c_64,c_66,c_606,c_629,c_638,c_647]) ).
cnf(c_671,plain,
( equilibrium(X0) != equilibrium(sK0)
| X0 != sK0
| ~ greater(equilibrium(X0),sK1) ),
inference(resolution_lifted,[status(thm)],[c_425,c_69]) ).
cnf(c_672,plain,
( equilibrium(sK0) != equilibrium(sK0)
| ~ greater(equilibrium(sK0),sK1) ),
inference(unflattening,[status(thm)],[c_671]) ).
cnf(c_673,plain,
equilibrium(sK0) != equilibrium(sK0),
inference(global_subsumption_just,[status(thm)],[c_672,c_523,c_543,c_648,c_672]) ).
cnf(c_679,plain,
iProver_spec_dis_eq_i(equilibrium(sK0),equilibrium(sK0)),
inference(dis_equality_elim,[status(thm)],[c_673]) ).
cnf(c_681,plain,
~ iProver_spec_dis_eq_i(X0,X0),
theory(irreflexivity) ).
cnf(c_691,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_679,c_681]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT024+1 : TPTP v8.1.2. Released v2.0.0.
% 0.12/0.13 % Command : run_iprover %s %d THM
% 0.14/0.34 % Computer : n031.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Mon Aug 28 06:34:39 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.20/0.45 Running first-order theorem proving
% 0.20/0.45 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.84/1.13 % SZS status Started for theBenchmark.p
% 0.84/1.13 % SZS status Theorem for theBenchmark.p
% 0.84/1.13
% 0.84/1.13 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.84/1.13
% 0.84/1.13 ------ iProver source info
% 0.84/1.13
% 0.84/1.13 git: date: 2023-05-31 18:12:56 +0000
% 0.84/1.13 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.84/1.13 git: non_committed_changes: false
% 0.84/1.13 git: last_make_outside_of_git: false
% 0.84/1.13
% 0.84/1.13 ------ Parsing...
% 0.84/1.13 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.84/1.13
% 0.84/1.13 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e
% 0.84/1.13
% 0.84/1.13 % SZS status Theorem for theBenchmark.p
% 0.84/1.13
% 0.84/1.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.84/1.13
% 0.84/1.13
%------------------------------------------------------------------------------