%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT027+1 : TPTP v9.3.1. Released v2.0.0.
% 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 : Theorem 2.45s 1.30s
% Output : CNFRefutation 2.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 13
% Syntax : Number of formulae : 138 ( 17 unt; 4 def)
% Number of atoms : 614 ( 46 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 724 ( 337 ~; 335 |; 40 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 15 ( 13 usr; 7 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 192 ( 0 sgn 183 !; 9 ?; 97 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ( ! [X2] :
( ( greater_or_equal(X2,X1)
& greater(cardinality_at_time(first_movers,X2),zero) )
=> greater(zero,growth_rate(first_movers,X2)) )
& in_environment(X0,X1)
& stable(X0)
& environment(X0) )
=> contracts_from(X1,first_movers) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_contracts_from) ).
fof(f2,axiom,
! [X0,X1] :
( ( greater(cardinality_at_time(efficient_producers,X1),zero)
& greater(cardinality_at_time(first_movers,X1),zero)
& in_environment(X0,X1)
& environment(X0) )
=> subpopulations(first_movers,efficient_producers,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep) ).
fof(f3,axiom,
! [X0,X1,X2] :
( ( greater(X2,X1)
& in_environment(X0,X1)
& stable(X0)
& environment(X0) )
=> in_environment(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_long_stable_environments) ).
fof(f4,axiom,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> in_environment(X0,appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_EP_in_stable_environments) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( greater(X1,X2)
& greater(X0,X1) )
=> greater(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_transitivity) ).
fof(f6,axiom,
! [X0,X1] :
( greater_or_equal(X0,X1)
<=> ( X0 = X1
| greater(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal) ).
fof(f7,axiom,
! [X0,X1] :
( ( greater_or_equal(X1,appear(efficient_producers,X0))
& in_environment(X0,X1)
& environment(X0) )
=> greater(cardinality_at_time(efficient_producers,X1),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6) ).
fof(f8,axiom,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( ! [X2] :
( ( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(zero,growth_rate(first_movers,X2)) )
& greater(X1,appear(efficient_producers,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l10) ).
fof(f9,conjecture,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( contracts_from(X1,first_movers)
& greater(X1,appear(efficient_producers,X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l9) ).
fof(f10,negated_conjecture,
~ ! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( contracts_from(X1,first_movers)
& greater(X1,appear(efficient_producers,X0)) ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ? [X2] :
( greater_or_equal(X2,X1)
& greater(cardinality_at_time(first_movers,X2),zero)
& ~ greater(zero,growth_rate(first_movers,X2)) )
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0)
| contracts_from(X1,first_movers) ),
inference(ennf_transformation,[],[f1]) ).
fof(f12,plain,
! [X0,X1] :
( ? [X2] :
( greater_or_equal(X2,X1)
& greater(cardinality_at_time(first_movers,X2),zero)
& ~ greater(zero,growth_rate(first_movers,X2)) )
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0)
| contracts_from(X1,first_movers) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f14,plain,
! [X0,X1] :
( ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ~ greater(X2,X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0)
| in_environment(X0,X2) ),
inference(ennf_transformation,[],[f3]) ).
fof(f16,plain,
! [X0,X1,X2] :
( ~ greater(X2,X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0)
| in_environment(X0,X2) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| in_environment(X0,appear(efficient_producers,X0)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f18,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| in_environment(X0,appear(efficient_producers,X0)) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ~ greater(X1,X2)
| ~ greater(X0,X1)
| greater(X0,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ greater(X1,X2)
| ~ greater(X0,X1)
| greater(X0,X2) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(ennf_transformation,[],[f7]) ).
fof(f22,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| ? [X1] :
( ! [X2] :
( ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(zero,growth_rate(first_movers,X2)) )
& greater(X1,appear(efficient_producers,X0)) ) ),
inference(ennf_transformation,[],[f8]) ).
fof(f24,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| ? [X1] :
( ! [X2] :
( ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(zero,growth_rate(first_movers,X2)) )
& greater(X1,appear(efficient_producers,X0)) ) ),
inference(flattening,[],[f23]) ).
fof(f25,plain,
? [X0] :
( stable(X0)
& environment(X0)
& ! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,X0)) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f26,plain,
? [X0] :
( stable(X0)
& environment(X0)
& ! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,X0)) ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ( greater_or_equal(sK0(X1),X1)
& greater(cardinality_at_time(first_movers,sK0(X1)),zero)
& ~ greater(zero,growth_rate(first_movers,sK0(X1))) )
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0)
| contracts_from(X1,first_movers) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X1))],[f12]) ).
fof(f28,plain,
! [X0,X1] :
( ( ~ greater_or_equal(X0,X1)
| X0 = X1
| greater(X0,X1) )
& ( ( X0 != X1
& ~ greater(X0,X1) )
| greater_or_equal(X0,X1) ) ),
inference(nnf_transformation,[],[f6]) ).
fof(f29,plain,
! [X0,X1] :
( ( ~ greater_or_equal(X0,X1)
| X0 = X1
| greater(X0,X1) )
& ( ( X0 != X1
& ~ greater(X0,X1) )
| greater_or_equal(X0,X1) ) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| ( ! [X2] :
( ~ greater_or_equal(X2,sK1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(zero,growth_rate(first_movers,X2)) )
& greater(sK1(X0),appear(efficient_producers,X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f24]) ).
fof(f31,plain,
( stable(sK2)
& environment(sK2)
& ! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,sK2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f26]) ).
fof(f32,plain,
! [X0,X1] :
( greater_or_equal(sK0(X1),X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0)
| contracts_from(X1,first_movers) ),
inference(cnf_transformation,[],[f27]) ).
fof(f33,plain,
! [X0,X1] :
( greater(cardinality_at_time(first_movers,sK0(X1)),zero)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0)
| contracts_from(X1,first_movers) ),
inference(cnf_transformation,[],[f27]) ).
fof(f34,plain,
! [X0,X1] :
( ~ greater(zero,growth_rate(first_movers,sK0(X1)))
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0)
| contracts_from(X1,first_movers) ),
inference(cnf_transformation,[],[f27]) ).
fof(f35,plain,
! [X0,X1] :
( ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ greater(X2,X1)
| ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0)
| in_environment(X0,X2) ),
inference(cnf_transformation,[],[f16]) ).
fof(f37,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| in_environment(X0,appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f18]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ greater(X1,X2)
| ~ greater(X0,X1)
| greater(X0,X2) ),
inference(cnf_transformation,[],[f20]) ).
fof(f39,plain,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| X0 = X1
| greater(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f41,plain,
! [X0,X1] :
( ~ greater(X0,X1)
| greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
fof(f42,plain,
! [X0,X1] :
( ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(cardinality_at_time(efficient_producers,X1),zero) ),
inference(cnf_transformation,[],[f22]) ).
fof(f43,plain,
! [X2,X0] :
( ~ stable(X0)
| ~ environment(X0)
| ~ greater_or_equal(X2,sK1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(zero,growth_rate(first_movers,X2)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f44,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| greater(sK1(X0),appear(efficient_producers,X0)) ),
inference(cnf_transformation,[],[f30]) ).
fof(f45,plain,
stable(sK2),
inference(cnf_transformation,[],[f31]) ).
fof(f46,plain,
environment(sK2),
inference(cnf_transformation,[],[f31]) ).
fof(f47,plain,
! [X1] :
( ~ contracts_from(X1,first_movers)
| ~ greater(X1,appear(efficient_producers,sK2)) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( contracts_from(X0,first_movers)
| ~ stable(X1)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(zero,growth_rate(first_movers,sK0(X0))) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( contracts_from(X1,first_movers)
| greater(cardinality_at_time(first_movers,sK0(X1)),zero)
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( contracts_from(X1,first_movers)
| greater_or_equal(sK0(X1),X1)
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( subpopulations(first_movers,efficient_producers,X1,X0)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater(cardinality_at_time(first_movers,X0),zero) ),
inference(cnf_transformation,[],[f35]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i] :
( in_environment(X0,X2)
| ~ stable(X0)
| ~ environment(X0)
| ~ greater(X2,X1)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_54,plain,
! [X0: $i] :
( in_environment(X0,appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(X2,X1)
| ~ greater(X2,X0)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( greater(X0,X1)
| ( X0 = X1 )
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater_or_equal(X0,appear(efficient_producers,X1)) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_60,plain,
! [X0: $i] :
( greater(sK1(X0),appear(efficient_producers,X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( greater(zero,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,[],[f43]) ).
tcf(c_62,negated_conjecture,
! [X0: $i] :
( ~ contracts_from(X0,first_movers)
| ~ greater(X0,appear(efficient_producers,sK2)) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_63,negated_conjecture,
environment(sK2),
inference(cnf_transformation,[],[f46]) ).
tcf(c_64,negated_conjecture,
stable(sK2),
inference(cnf_transformation,[],[f45]) ).
tcf(c_293,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( greater(zero,growth_rate(first_movers,X1))
| ~ stable(X3)
| ~ environment(X3)
| ~ environment(X2)
| ~ in_environment(X2,X0)
| ~ greater_or_equal(X1,sK1(X3))
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater(cardinality_at_time(first_movers,X0),zero)
| ( efficient_producers != efficient_producers )
| ( first_movers != first_movers )
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_61]) ).
tcf(c_294,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X0))
| ~ stable(X1)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater_or_equal(X0,sK1(X1))
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater(cardinality_at_time(first_movers,X0),zero) ),
inference(unflattening,[status(thm)],[c_293]) ).
tcf(c_324,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ stable(X2)
| ~ environment(X2)
| ~ in_environment(X2,X0)
| ~ greater(X1,appear(efficient_producers,sK2))
| ~ greater(zero,growth_rate(first_movers,sK0(X0)))
| ( first_movers != first_movers )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_62]) ).
tcf(c_325,plain,
! [X0: $i,X1: $i] :
( ~ stable(X1)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(X0,appear(efficient_producers,sK2))
| ~ greater(zero,growth_rate(first_movers,sK0(X0))) ),
inference(unflattening,[status(thm)],[c_324]) ).
tcf(c_342,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater_or_equal(sK0(X1),X1)
| ~ stable(X2)
| ~ environment(X2)
| ~ in_environment(X2,X1)
| ~ greater(X0,appear(efficient_producers,sK2))
| ( first_movers != first_movers )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_62,c_51]) ).
tcf(c_343,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(sK0(X0),X0)
| ~ stable(X1)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(X0,appear(efficient_producers,sK2)) ),
inference(unflattening,[status(thm)],[c_342]) ).
tcf(c_360,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(cardinality_at_time(first_movers,sK0(X1)),zero)
| ~ stable(X2)
| ~ environment(X2)
| ~ in_environment(X2,X1)
| ~ greater(X0,appear(efficient_producers,sK2))
| ( first_movers != first_movers )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_62,c_50]) ).
tcf(c_361,plain,
! [X0: $i,X1: $i] :
( greater(cardinality_at_time(first_movers,sK0(X0)),zero)
| ~ stable(X1)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(X0,appear(efficient_producers,sK2)) ),
inference(unflattening,[status(thm)],[c_360]) ).
tcf(c_393,plain,
! [X0: $i,X1: $i] :
( greater(cardinality_at_time(first_movers,sK0(X1)),zero)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(X1,appear(efficient_producers,sK2))
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_361,c_64]) ).
tcf(c_394,plain,
! [X0: $i] :
( greater(cardinality_at_time(first_movers,sK0(X0)),zero)
| ~ environment(sK2)
| ~ in_environment(sK2,X0)
| ~ greater(X0,appear(efficient_producers,sK2)) ),
inference(unflattening,[status(thm)],[c_393]) ).
tcf(c_396,plain,
! [X0: $i] :
( greater(cardinality_at_time(first_movers,sK0(X0)),zero)
| ~ greater(X0,appear(efficient_producers,sK2))
| ~ in_environment(sK2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_394,c_63,c_394]) ).
tcf(c_397,plain,
! [X0: $i] :
( greater(cardinality_at_time(first_movers,sK0(X0)),zero)
| ~ in_environment(sK2,X0)
| ~ greater(X0,appear(efficient_producers,sK2)) ),
inference(renaming,[status(thm)],[c_396]) ).
tcf(c_408,plain,
! [X0: $i,X1: $i] :
( greater_or_equal(sK0(X1),X1)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(X1,appear(efficient_producers,sK2))
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_343,c_64]) ).
tcf(c_409,plain,
! [X0: $i] :
( greater_or_equal(sK0(X0),X0)
| ~ environment(sK2)
| ~ in_environment(sK2,X0)
| ~ greater(X0,appear(efficient_producers,sK2)) ),
inference(unflattening,[status(thm)],[c_408]) ).
tcf(c_411,plain,
! [X0: $i] :
( greater_or_equal(sK0(X0),X0)
| ~ greater(X0,appear(efficient_producers,sK2))
| ~ in_environment(sK2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_409,c_63,c_409]) ).
tcf(c_412,plain,
! [X0: $i] :
( greater_or_equal(sK0(X0),X0)
| ~ in_environment(sK2,X0)
| ~ greater(X0,appear(efficient_producers,sK2)) ),
inference(renaming,[status(thm)],[c_411]) ).
tcf(c_423,plain,
! [X0: $i,X1: $i] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(X1,appear(efficient_producers,sK2))
| ~ greater(zero,growth_rate(first_movers,sK0(X1)))
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_325,c_64]) ).
tcf(c_424,plain,
! [X0: $i] :
( ~ environment(sK2)
| ~ in_environment(sK2,X0)
| ~ greater(X0,appear(efficient_producers,sK2))
| ~ greater(zero,growth_rate(first_movers,sK0(X0))) ),
inference(unflattening,[status(thm)],[c_423]) ).
tcf(c_426,plain,
! [X0: $i] :
( ~ greater(zero,growth_rate(first_movers,sK0(X0)))
| ~ greater(X0,appear(efficient_producers,sK2))
| ~ in_environment(sK2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_424,c_63,c_424]) ).
tcf(c_427,plain,
! [X0: $i] :
( ~ in_environment(sK2,X0)
| ~ greater(X0,appear(efficient_producers,sK2))
| ~ greater(zero,growth_rate(first_movers,sK0(X0))) ),
inference(renaming,[status(thm)],[c_426]) ).
tcf(c_438,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X1))
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater_or_equal(X1,sK1(X0))
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_294,c_64]) ).
tcf(c_439,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| ~ environment(sK2)
| ~ in_environment(sK2,X0)
| ~ greater_or_equal(X0,sK1(sK2))
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater(cardinality_at_time(first_movers,X0),zero) ),
inference(unflattening,[status(thm)],[c_438]) ).
tcf(c_441,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| ~ greater(cardinality_at_time(first_movers,X0),zero)
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater_or_equal(X0,sK1(sK2))
| ~ in_environment(sK2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_439,c_63,c_439]) ).
tcf(c_442,plain,
! [X0: $i] :
( greater(zero,growth_rate(first_movers,X0))
| ~ in_environment(sK2,X0)
| ~ greater_or_equal(X0,sK1(sK2))
| ~ greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater(cardinality_at_time(first_movers,X0),zero) ),
inference(renaming,[status(thm)],[c_441]) ).
tcf(c_459,plain,
! [X0: $i] :
( greater(sK1(X0),appear(efficient_producers,X0))
| ~ environment(X0)
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_60,c_64]) ).
tcf(c_460,plain,
( greater(sK1(sK2),appear(efficient_producers,sK2))
| ~ environment(sK2) ),
inference(unflattening,[status(thm)],[c_459]) ).
tcf(c_461,plain,
greater(sK1(sK2),appear(efficient_producers,sK2)),
inference(global_subsumption_just,[status(thm)],[c_460,c_63,c_460]) ).
tcf(c_466,plain,
! [X0: $i] :
( in_environment(X0,appear(efficient_producers,X0))
| ~ environment(X0)
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_64]) ).
tcf(c_467,plain,
( in_environment(sK2,appear(efficient_producers,sK2))
| ~ environment(sK2) ),
inference(unflattening,[status(thm)],[c_466]) ).
tcf(c_468,plain,
in_environment(sK2,appear(efficient_producers,sK2)),
inference(global_subsumption_just,[status(thm)],[c_467,c_63,c_467]) ).
tcf(c_473,plain,
! [X0: $i,X1: $i,X2: $i] :
( in_environment(X0,X2)
| ~ environment(X0)
| ~ greater(X2,X1)
| ~ in_environment(X0,X1)
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_64]) ).
tcf(c_474,plain,
! [X0: $i,X1: $i] :
( in_environment(sK2,X0)
| ~ environment(sK2)
| ~ in_environment(sK2,X1)
| ~ greater(X0,X1) ),
inference(unflattening,[status(thm)],[c_473]) ).
tcf(c_475,plain,
! [X0: $i,X1: $i] :
( in_environment(sK2,X0)
| ~ greater(X0,X1)
| ~ in_environment(sK2,X1) ),
inference(global_subsumption_just,[status(thm)],[c_474,c_63,c_474]) ).
tcf(c_476,plain,
! [X0: $i,X1: $i] :
( in_environment(sK2,X0)
| ~ in_environment(sK2,X1)
| ~ greater(X0,X1) ),
inference(renaming,[status(thm)],[c_475]) ).
tcf(c_505,plain,
! [X0: $i,X1: $i] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ in_environment(X0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_63]) ).
tcf(c_506,plain,
! [X0: $i] :
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ in_environment(sK2,X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sK2)) ),
inference(unflattening,[status(thm)],[c_505]) ).
tcf(c_522,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(X1,X2)
| ( X1 = X2 )
| ~ in_environment(sK2,X0)
| ~ greater(X0,appear(efficient_producers,sK2))
| ( X0 != X2 )
| ( sK0(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_412,c_58]) ).
tcf(c_523,plain,
! [X0: $i] :
( greater(sK0(X0),X0)
| ( sK0(X0) = X0 )
| ~ in_environment(sK2,X0)
| ~ greater(X0,appear(efficient_producers,sK2)) ),
inference(unflattening,[status(thm)],[c_522]) ).
tcf(c_537,plain,
! [X0: $i,X1: $i] :
( greater(zero,growth_rate(first_movers,X1))
| ~ in_environment(sK2,X1)
| ~ in_environment(sK2,X0)
| ~ greater(X0,appear(efficient_producers,sK2))
| ~ greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(cardinality_at_time(first_movers,X1),zero)
| ( sK1(sK2) != X0 )
| ( sK0(X0) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_412,c_442]) ).
tcf(c_538,plain,
( greater(zero,growth_rate(first_movers,sK0(sK1(sK2))))
| ~ in_environment(sK2,sK1(sK2))
| ~ in_environment(sK2,sK0(sK1(sK2)))
| ~ greater(sK1(sK2),appear(efficient_producers,sK2))
| ~ greater(cardinality_at_time(efficient_producers,sK0(sK1(sK2))),zero)
| ~ greater(cardinality_at_time(first_movers,sK0(sK1(sK2))),zero) ),
inference(unflattening,[status(thm)],[c_537]) ).
tcf(c_539,plain,
( greater(zero,growth_rate(first_movers,sK0(sK1(sK2))))
| ~ in_environment(sK2,sK1(sK2))
| ~ in_environment(sK2,sK0(sK1(sK2)))
| ~ greater(cardinality_at_time(first_movers,sK0(sK1(sK2))),zero)
| ~ greater(cardinality_at_time(efficient_producers,sK0(sK1(sK2))),zero) ),
inference(global_subsumption_just,[status(thm)],[c_538,c_63,c_460,c_538]) ).
tcf(c_540,plain,
( greater(zero,growth_rate(first_movers,sK0(sK1(sK2))))
| ~ in_environment(sK2,sK1(sK2))
| ~ in_environment(sK2,sK0(sK1(sK2)))
| ~ greater(cardinality_at_time(efficient_producers,sK0(sK1(sK2))),zero)
| ~ greater(cardinality_at_time(first_movers,sK0(sK1(sK2))),zero) ),
inference(renaming,[status(thm)],[c_539]) ).
tcf(c_589,plain,
! [X0: $i,X1: $i,X2: $i] :
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ in_environment(sK2,X1)
| ~ greater(X0,X2)
| ( X0 != X1 )
| ( appear(efficient_producers,sK2) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_506]) ).
tcf(c_590,plain,
! [X0: $i] :
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ in_environment(sK2,X0)
| ~ greater(X0,appear(efficient_producers,sK2)) ),
inference(unflattening,[status(thm)],[c_589]) ).
tcf(c_812,definition,
iPr_def_18 = sK0(iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_18])],[]) ).
tcf(c_813,definition,
iPr_def_19 = cardinality_at_time(first_movers,iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_19])],[]) ).
tcf(c_814,definition,
iPr_def_20 = cardinality_at_time(efficient_producers,iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_20])],[]) ).
tcf(c_815,definition,
iPr_def_21 = growth_rate(first_movers,iPr_def_18),
introduced(definition,[new_symbols(definition,[iPr_def_21])],[]) ).
tcf(c_818,plain,
! [X0: $i] :
( greater(cardinality_at_time(efficient_producers,X0),zero)
| ~ greater(X0,iPr_def_10)
| ~ in_environment(sK2,X0) ),
inference(demodulation,[status(thm)],[c_590]) ).
tcf(c_821,plain,
( greater(zero,iPr_def_21)
| ~ greater(iPr_def_20,zero)
| ~ greater(iPr_def_19,zero)
| ~ in_environment(sK2,iPr_def_18)
| ~ in_environment(sK2,iPr_def_12) ),
inference(demodulation,[status(thm)],[c_540,c_815,c_814,c_812,c_813]) ).
tcf(c_822,plain,
! [X0: $i] :
( greater(sK0(X0),X0)
| ( sK0(X0) = X0 )
| ~ greater(X0,iPr_def_10)
| ~ in_environment(sK2,X0) ),
inference(demodulation,[status(thm)],[c_523]) ).
tcf(c_823,plain,
! [X0: $i,X1: $i] :
( in_environment(sK2,X0)
| ~ in_environment(sK2,X1)
| ~ greater(X0,X1) ),
inference(demodulation,[status(thm)],[c_476]) ).
tcf(c_824,plain,
in_environment(sK2,iPr_def_10),
inference(demodulation,[status(thm)],[c_468]) ).
tcf(c_825,plain,
greater(iPr_def_12,iPr_def_10),
inference(demodulation,[status(thm)],[c_461]) ).
tcf(c_826,plain,
! [X0: $i] :
( ~ greater(X0,iPr_def_10)
| ~ in_environment(sK2,X0)
| ~ greater(zero,growth_rate(first_movers,sK0(X0))) ),
inference(demodulation,[status(thm)],[c_427]) ).
tcf(c_827,plain,
! [X0: $i] :
( greater(cardinality_at_time(first_movers,sK0(X0)),zero)
| ~ greater(X0,iPr_def_10)
| ~ in_environment(sK2,X0) ),
inference(demodulation,[status(thm)],[c_397]) ).
tcf(c_1159,plain,
( in_environment(sK2,iPr_def_12)
| ~ in_environment(sK2,iPr_def_10) ),
inference(superposition,[status(thm)],[c_825,c_823]) ).
tcf(c_1160,plain,
in_environment(sK2,iPr_def_12),
inference(forward_subsumption_resolution,[status(thm)],[c_1159,c_824]) ).
tcf(c_1194,plain,
( ~ greater(iPr_def_12,iPr_def_10)
| ~ in_environment(sK2,iPr_def_12)
| ~ greater(zero,growth_rate(first_movers,iPr_def_18)) ),
inference(superposition,[status(thm)],[c_812,c_826]) ).
tcf(c_1195,plain,
( greater(cardinality_at_time(first_movers,iPr_def_18),zero)
| ~ greater(iPr_def_12,iPr_def_10)
| ~ in_environment(sK2,iPr_def_12) ),
inference(superposition,[status(thm)],[c_812,c_827]) ).
tcf(c_1196,plain,
( greater(iPr_def_19,zero)
| ~ greater(iPr_def_12,iPr_def_10)
| ~ in_environment(sK2,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_1195,c_813]) ).
tcf(c_1197,plain,
greater(iPr_def_19,zero),
inference(forward_subsumption_resolution,[status(thm)],[c_1196,c_825,c_1160]) ).
tcf(c_1198,plain,
( ~ greater(iPr_def_12,iPr_def_10)
| ~ greater(zero,iPr_def_21)
| ~ in_environment(sK2,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_1194,c_815]) ).
tcf(c_1199,plain,
~ greater(zero,iPr_def_21),
inference(forward_subsumption_resolution,[status(thm)],[c_1198,c_825,c_1160]) ).
tcf(c_1257,plain,
( greater(iPr_def_20,zero)
| ~ greater(iPr_def_18,iPr_def_10)
| ~ in_environment(sK2,iPr_def_18) ),
inference(superposition,[status(thm)],[c_814,c_818]) ).
tcf(c_1331,plain,
( greater(iPr_def_18,iPr_def_12)
| ( sK0(iPr_def_12) = iPr_def_12 )
| ~ greater(iPr_def_12,iPr_def_10)
| ~ in_environment(sK2,iPr_def_12) ),
inference(superposition,[status(thm)],[c_812,c_822]) ).
tcf(c_1334,plain,
( greater(iPr_def_18,iPr_def_12)
| ( iPr_def_12 = iPr_def_18 )
| ~ greater(iPr_def_12,iPr_def_10)
| ~ in_environment(sK2,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_1331,c_812]) ).
tcf(c_1335,plain,
( greater(iPr_def_18,iPr_def_12)
| ( iPr_def_12 = iPr_def_18 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1334,c_825,c_1160]) ).
tcf(c_1357,plain,
! [X0: $i] :
( greater(iPr_def_18,X0)
| ( iPr_def_12 = iPr_def_18 )
| ~ greater(iPr_def_12,X0) ),
inference(superposition,[status(thm)],[c_1335,c_55]) ).
tcf(c_1358,plain,
( in_environment(sK2,iPr_def_18)
| ( iPr_def_12 = iPr_def_18 )
| ~ in_environment(sK2,iPr_def_12) ),
inference(superposition,[status(thm)],[c_1335,c_823]) ).
tcf(c_1359,plain,
( in_environment(sK2,iPr_def_18)
| ( iPr_def_12 = iPr_def_18 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1358,c_1160]) ).
tcf(c_1441,plain,
( ~ in_environment(sK2,iPr_def_18)
| ~ greater(iPr_def_18,iPr_def_10) ),
inference(global_subsumption_just,[status(thm)],[c_1257,c_821,c_1160,c_1197,c_1199,c_1257]) ).
tcf(c_1442,plain,
( ~ greater(iPr_def_18,iPr_def_10)
| ~ in_environment(sK2,iPr_def_18) ),
inference(renaming,[status(thm)],[c_1441]) ).
tcf(c_1453,plain,
( greater(iPr_def_18,iPr_def_10)
| ( iPr_def_12 = iPr_def_18 ) ),
inference(superposition,[status(thm)],[c_825,c_1357]) ).
tcf(c_1463,plain,
iPr_def_12 = iPr_def_18,
inference(global_subsumption_just,[status(thm)],[c_1359,c_821,c_1160,c_1197,c_1199,c_1257,c_1359,c_1453]) ).
tcf(c_1466,plain,
( ~ greater(iPr_def_12,iPr_def_10)
| ~ in_environment(sK2,iPr_def_12) ),
inference(demodulation,[status(thm)],[c_1442,c_1463]) ).
tcf(c_1474,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1466,c_825,c_1160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT027+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 % Computer : n002.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Thu Sep 24 01:06:49 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.42 Running first-order theorem proving
% 0.12/0.42 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
% 0.12/0.44
% 0.12/0.44 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.44
% 0.12/0.44 % Detected problem language: tptp
% 0.12/0.45 % Proving...
% 2.45/1.30 % SZS status Started for theBenchmark.p
% 2.45/1.30 % SZS status Theorem for theBenchmark.p
% 2.45/1.30
% 2.45/1.30 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.45/1.30
% 2.45/1.30 % ------ iProver source info
% 2.45/1.30
% 2.45/1.30 % git: date: 2026-07-19 20:42:38 +0200
% 2.45/1.30 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.45/1.30 % git: non_committed_changes: false
% 2.45/1.30
% 2.45/1.30 % ------ Parsing...
% 2.45/1.30 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.45/1.30
% 2.45/1.30 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 6 0s sf_e pe_s pe_e %
% 2.45/1.30
% 2.45/1.30 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.45/1.30
% 2.45/1.30 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.45/1.30 % ------ Proving...
% 2.45/1.30 % ------ Problem Properties
% 2.45/1.30
% 2.45/1.30 %
% 2.45/1.30 % clauses 25
% 2.45/1.30 % conjectures 0
% 2.45/1.30 % EPR 8
% 2.45/1.30 % Horn 24
% 2.45/1.30 % unary 15
% 2.45/1.30 % binary 0
% 2.45/1.30 % lits 51
% 2.45/1.30 % lits eq 13
% 2.45/1.30 % fd_pure 0
% 2.45/1.30 % fd_pseudo 0
% 2.45/1.30 % fd_cond 0
% 2.45/1.30 % fd_pseudo_cond 0
% 2.45/1.30 % AC symbols 0
% 2.45/1.30
% 2.45/1.30 % ------ Schedule dynamic 5 is on
% 2.45/1.30
% 2.45/1.30 % ------ no conjectures: strip conj schedule
% 2.45/1.30
% 2.45/1.30 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
% 2.45/1.30
% 2.45/1.30
% 2.45/1.30 % ------
% 2.45/1.30 % Current options:
% 2.45/1.30 % ------
% 2.45/1.30
% 2.45/1.30
% 2.45/1.30 %
% 2.45/1.30
% 2.45/1.30 % ------ Proving...
% 2.45/1.30 %
% 2.45/1.30
% 2.45/1.30 % SZS status Theorem for theBenchmark.p
% 2.45/1.30
% 2.45/1.30 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.45/1.31
% 2.45/1.31
%------------------------------------------------------------------------------