%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT024-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n002.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 02:12:24 PM UTC 2026
% Result : Unsatisfiable 1.42s 1.30s
% Output : CNFRefutation 1.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 20
% Syntax : Number of formulae : 92 ( 11 unt; 0 def)
% Number of atoms : 406 ( 103 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 549 ( 235 ~; 314 |; 0 &)
% ( 0 <=>; 0 =>; 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 : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 107 ( 0 sgn 107 !; 0 ?; 65 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occur_24) ).
fof(f2,axiom,
! [X0,X1] :
( greater(number_of_organizations(X0,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_number_of_organizations_25) ).
fof(f3,axiom,
! [X0,X1] :
( ~ greater(equilibrium(X0),X1)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_equilibrium_26) ).
fof(f5,axiom,
! [X0,X1] :
( constant(resources(X0,X1))
| greater(equilibrium(X0),X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a3_28) ).
fof(f7,axiom,
! [X0,X1] :
( constant(number_of_organizations(X0,X1))
| ~ constant(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a6_30) ).
fof(f8,axiom,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| growth_rate(first_movers,X1) = zero
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l7_31) ).
fof(f9,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(reorient_equations,[],[f8]) ).
fof(f10,axiom,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| growth_rate(first_movers,X1) = zero
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l7_32) ).
fof(f11,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(reorient_equations,[],[f10]) ).
fof(f12,axiom,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(zero,growth_rate(efficient_producers,X1))
| growth_rate(first_movers,X1) = zero
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l7_33) ).
fof(f13,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(reorient_equations,[],[f12]) ).
fof(f14,axiom,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(efficient_producers,X1))
| growth_rate(first_movers,X1) = zero
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l7_34) ).
fof(f15,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(reorient_equations,[],[f14]) ).
fof(f16,axiom,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(growth_rate(first_movers,X1),zero)
| growth_rate(efficient_producers,X1) = zero
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l7_35) ).
fof(f17,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(reorient_equations,[],[f16]) ).
fof(f18,axiom,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(growth_rate(first_movers,X1),zero)
| growth_rate(efficient_producers,X1) = zero
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l7_36) ).
fof(f19,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(reorient_equations,[],[f18]) ).
fof(f20,axiom,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),zero)
| greater(zero,growth_rate(efficient_producers,X1))
| growth_rate(efficient_producers,X1) = zero
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l7_37) ).
fof(f21,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(reorient_equations,[],[f20]) ).
fof(f22,axiom,
! [X0,X1] :
( greater(zero,growth_rate(first_movers,X1))
| greater(zero,growth_rate(efficient_producers,X1))
| growth_rate(efficient_producers,X1) = zero
| ~ constant(number_of_organizations(X0,X1))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l7_38) ).
fof(f23,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(reorient_equations,[],[f22]) ).
fof(f24,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l6_39) ).
fof(f25,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l6_40) ).
fof(f26,negated_conjecture,
greater_or_equal(sk2,equilibrium(sk1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l6_41) ).
fof(f27,negated_conjecture,
( growth_rate(efficient_producers,sk2) != zero
| growth_rate(first_movers,sk2) != zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l6_42) ).
fof(f28,plain,
( zero != growth_rate(efficient_producers,sk2)
| zero != growth_rate(first_movers,sk2) ),
inference(reorient_equations,[],[f27]) ).
fof(f29,negated_conjecture,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(growth_rate(first_movers,sk2),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l6_43) ).
fof(f30,negated_conjecture,
( ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater(growth_rate(efficient_producers,sk2),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l6_44) ).
tcf(c_70,plain,
! [X0: $i,X1: $i] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( greater(number_of_organizations(X0,X1),zero)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_72,plain,
! [X0: $i,X1: $i] :
( ~ environment(X0)
| ~ greater_or_equal(X1,equilibrium(X0))
| ~ greater(equilibrium(X0),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_74,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,[],[f5]) ).
tcf(c_76,plain,
! [X0: $i,X1: $i] :
( constant(number_of_organizations(X0,X1))
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ constant(resources(X0,X1)) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_77,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,[],[f9]) ).
tcf(c_78,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,[],[f11]) ).
tcf(c_79,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,[],[f13]) ).
tcf(c_80,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,[],[f15]) ).
tcf(c_81,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,[],[f17]) ).
tcf(c_82,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,[],[f19]) ).
tcf(c_83,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,[],[f21]) ).
tcf(c_84,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,[],[f23]) ).
tcf(c_85,negated_conjecture,
environment(sk1),
inference(cnf_transformation,[],[f24]) ).
tcf(c_86,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(cnf_transformation,[],[f25]) ).
tcf(c_87,negated_conjecture,
greater_or_equal(sk2,equilibrium(sk1)),
inference(cnf_transformation,[],[f26]) ).
tcf(c_88,negated_conjecture,
( ( growth_rate(efficient_producers,sk2) != zero )
| ( growth_rate(first_movers,sk2) != zero ) ),
inference(cnf_transformation,[],[f28]) ).
tcf(c_89,negated_conjecture,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater(growth_rate(first_movers,sk2),zero) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_90,negated_conjecture,
( ~ greater(zero,growth_rate(first_movers,sk2))
| ~ greater(growth_rate(efficient_producers,sk2),zero) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_445,plain,
! [X0: $i,X1: $i] :
( ~ environment(X0)
| ~ greater(equilibrium(X0),X1)
| ( X1 != sk2 )
| ( equilibrium(X0) != equilibrium(sk1) ) ),
inference(resolution_lifted,[status(thm)],[c_72,c_87]) ).
tcf(c_446,plain,
! [X0: $i] :
( ~ environment(X0)
| ~ greater(equilibrium(X0),sk2)
| ( equilibrium(X0) != equilibrium(sk1) ) ),
inference(unflattening,[status(thm)],[c_445]) ).
tcf(c_460,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_70,c_76]) ).
tcf(c_461,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_460]) ).
tcf(c_490,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_70,c_74]) ).
tcf(c_491,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_490]) ).
tcf(c_493,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_491,c_71,c_491]) ).
tcf(c_552,plain,
! [X0: $i,X1: $i] :
( constant(resources(X0,X1))
| greater(equilibrium(X0),X1)
| ~ environment(X0)
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( X1 != sk2 )
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_493,c_86]) ).
tcf(c_553,plain,
( constant(resources(sk1,sk2))
| greater(equilibrium(sk1),sk2)
| ~ environment(sk1) ),
inference(unflattening,[status(thm)],[c_552]) ).
tcf(c_554,plain,
( constant(resources(sk1,sk2))
| greater(equilibrium(sk1),sk2) ),
inference(global_subsumption_just,[status(thm)],[c_553,c_85,c_553]) ).
tcf(c_572,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 != sk2 )
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_461,c_86]) ).
tcf(c_573,plain,
( constant(number_of_organizations(sk1,sk2))
| ~ environment(sk1)
| ~ constant(resources(sk1,sk2)) ),
inference(unflattening,[status(thm)],[c_572]) ).
tcf(c_574,plain,
( constant(number_of_organizations(sk1,sk2))
| ~ constant(resources(sk1,sk2)) ),
inference(global_subsumption_just,[status(thm)],[c_573,c_85,c_573]) ).
tcf(c_582,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 != sk2 )
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_84,c_86]) ).
tcf(c_583,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| greater(zero,growth_rate(first_movers,sk2))
| ( growth_rate(efficient_producers,sk2) = zero )
| ~ environment(sk1)
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(unflattening,[status(thm)],[c_582]) ).
tcf(c_584,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| greater(zero,growth_rate(first_movers,sk2))
| ( growth_rate(efficient_producers,sk2) = zero )
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(global_subsumption_just,[status(thm)],[c_583,c_85,c_583]) ).
tcf(c_598,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 != sk2 )
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_83,c_86]) ).
tcf(c_599,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| greater(growth_rate(efficient_producers,sk2),zero)
| ( growth_rate(efficient_producers,sk2) = zero )
| ~ environment(sk1)
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(unflattening,[status(thm)],[c_598]) ).
tcf(c_600,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| ~ constant(number_of_organizations(sk1,sk2))
| ( growth_rate(efficient_producers,sk2) = zero ) ),
inference(global_subsumption_just,[status(thm)],[c_599,c_85,c_90,c_584,c_599]) ).
tcf(c_601,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| ( growth_rate(efficient_producers,sk2) = zero )
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(renaming,[status(thm)],[c_600]) ).
tcf(c_611,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 != sk2 )
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_82,c_86]) ).
tcf(c_612,plain,
( greater(zero,growth_rate(first_movers,sk2))
| greater(growth_rate(first_movers,sk2),zero)
| ( growth_rate(efficient_producers,sk2) = zero )
| ~ environment(sk1)
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(unflattening,[status(thm)],[c_611]) ).
tcf(c_613,plain,
( greater(zero,growth_rate(first_movers,sk2))
| ~ constant(number_of_organizations(sk1,sk2))
| ( growth_rate(efficient_producers,sk2) = zero ) ),
inference(global_subsumption_just,[status(thm)],[c_612,c_85,c_90,c_89,c_584,c_599,c_612]) ).
tcf(c_614,plain,
( greater(zero,growth_rate(first_movers,sk2))
| ( growth_rate(efficient_producers,sk2) = zero )
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(renaming,[status(thm)],[c_613]) ).
tcf(c_624,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 != sk2 )
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_81,c_86]) ).
tcf(c_625,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| greater(growth_rate(first_movers,sk2),zero)
| ( growth_rate(efficient_producers,sk2) = zero )
| ~ environment(sk1)
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(unflattening,[status(thm)],[c_624]) ).
tcf(c_626,plain,
( ( growth_rate(efficient_producers,sk2) = zero )
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(global_subsumption_just,[status(thm)],[c_625,c_85,c_90,c_89,c_601,c_614,c_625]) ).
tcf(c_634,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 != sk2 )
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_80,c_86]) ).
tcf(c_635,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| greater(zero,growth_rate(first_movers,sk2))
| ( growth_rate(first_movers,sk2) = zero )
| ~ environment(sk1)
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(unflattening,[status(thm)],[c_634]) ).
tcf(c_636,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| greater(zero,growth_rate(first_movers,sk2))
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(global_subsumption_just,[status(thm)],[c_635,c_85,c_88,c_626,c_635]) ).
tcf(c_647,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 != sk2 )
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_79,c_86]) ).
tcf(c_648,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| greater(growth_rate(efficient_producers,sk2),zero)
| ( growth_rate(first_movers,sk2) = zero )
| ~ environment(sk1)
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(unflattening,[status(thm)],[c_647]) ).
tcf(c_649,plain,
( greater(zero,growth_rate(efficient_producers,sk2))
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(global_subsumption_just,[status(thm)],[c_648,c_85,c_90,c_88,c_626,c_636,c_648]) ).
tcf(c_657,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 != sk2 )
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_78,c_86]) ).
tcf(c_658,plain,
( greater(zero,growth_rate(first_movers,sk2))
| greater(growth_rate(first_movers,sk2),zero)
| ( growth_rate(first_movers,sk2) = zero )
| ~ environment(sk1)
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(unflattening,[status(thm)],[c_657]) ).
tcf(c_659,plain,
( greater(zero,growth_rate(first_movers,sk2))
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(global_subsumption_just,[status(thm)],[c_658,c_85,c_89,c_88,c_626,c_649,c_658]) ).
tcf(c_667,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 != sk2 )
| ( X0 != sk1 ) ),
inference(resolution_lifted,[status(thm)],[c_77,c_86]) ).
tcf(c_668,plain,
( greater(growth_rate(efficient_producers,sk2),zero)
| greater(growth_rate(first_movers,sk2),zero)
| ( growth_rate(first_movers,sk2) = zero )
| ~ environment(sk1)
| ~ constant(number_of_organizations(sk1,sk2)) ),
inference(unflattening,[status(thm)],[c_667]) ).
tcf(c_669,plain,
~ constant(number_of_organizations(sk1,sk2)),
inference(global_subsumption_just,[status(thm)],[c_668,c_85,c_90,c_89,c_88,c_626,c_649,c_659,c_668]) ).
tcf(c_692,plain,
! [X0: $i] :
( ~ greater(equilibrium(X0),sk2)
| ( X0 != sk1 )
| ( equilibrium(X0) != equilibrium(sk1) ) ),
inference(resolution_lifted,[status(thm)],[c_446,c_85]) ).
tcf(c_693,plain,
( ~ greater(equilibrium(sk1),sk2)
| ( equilibrium(sk1) != equilibrium(sk1) ) ),
inference(unflattening,[status(thm)],[c_692]) ).
tcf(c_694,plain,
equilibrium(sk1) != equilibrium(sk1),
inference(global_subsumption_just,[status(thm)],[c_693,c_554,c_574,c_669,c_693]) ).
tcf(c_700,plain,
iProver_spec_dis_eq_i(equilibrium(sk1),equilibrium(sk1)),
inference(dis_equality_elim,[status(thm)],[c_694]) ).
tcf(c_702,plain,
! [X0: $i] : ~ iProver_spec_dis_eq_i(X0,X0),
theory(irreflexivity) ).
tcf(c_712,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_700,c_702]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT024-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n002.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 01:06:19 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.45 % Proving...
% 1.42/1.30 % SZS status Started for theBenchmark.p
% 1.42/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 1.42/1.30
% 1.42/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.42/1.30
% 1.42/1.30 % ------ iProver source info
% 1.42/1.30
% 1.42/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 1.42/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.42/1.30 % git: non_committed_changes: false
% 1.42/1.30
% 1.42/1.30 % ------ Parsing...% successful
% 1.42/1.30
% 1.42/1.30
% 1.42/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.42/1.30
% 1.42/1.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e %
% 1.42/1.30
% 1.42/1.30 % SZS status Unsatisfiable for theBenchmark.p
% 1.42/1.30
% 1.42/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.42/1.30
% 1.42/1.30
%------------------------------------------------------------------------------