TSTP Solution File: MGT023+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : MGT023+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n027.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 09:14:15 EDT 2023
% Result : Theorem 0.80s 1.20s
% Output : CNFRefutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 57 ( 10 unt; 0 def)
% Number of atoms : 242 ( 40 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 311 ( 126 ~; 136 |; 40 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 76 ( 0 sgn; 34 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ( ! [X2] :
( ( greater(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& in_environment(X0,X1)
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& environment(X0) )
=> critical_point(X0) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
fof(f2,axiom,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( ! [X2] :
( ( greater(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& in_environment(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12) ).
fof(f3,conjecture,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> in_environment(X0,critical_point(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5) ).
fof(f4,negated_conjecture,
~ ! [X0] :
( ( stable(X0)
& environment(X0) )
=> in_environment(X0,critical_point(X0)) ),
inference(negated_conjecture,[],[f3]) ).
fof(f5,plain,
! [X0,X1] :
( critical_point(X0) = X1
| ? [X2] :
( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& greater(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f6,plain,
! [X0,X1] :
( critical_point(X0) = X1
| ? [X2] :
( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& greater(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& in_environment(X0,X1) )
| ~ stable(X0)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f8,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& in_environment(X0,X1) )
| ~ stable(X0)
| ~ environment(X0) ),
inference(flattening,[],[f7]) ).
fof(f9,plain,
? [X0] :
( ~ in_environment(X0,critical_point(X0))
& stable(X0)
& environment(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,plain,
? [X0] :
( ~ in_environment(X0,critical_point(X0))
& stable(X0)
& environment(X0) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ? [X2] :
( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& greater(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> ( ~ greater(growth_rate(efficient_producers,sK0(X0,X1)),growth_rate(first_movers,sK0(X0,X1)))
& greater(sK0(X0,X1),X1)
& subpopulations(first_movers,efficient_producers,X0,sK0(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f12,plain,
! [X0,X1] :
( critical_point(X0) = X1
| ( ~ greater(growth_rate(efficient_producers,sK0(X0,X1)),growth_rate(first_movers,sK0(X0,X1)))
& greater(sK0(X0,X1),X1)
& subpopulations(first_movers,efficient_producers,X0,sK0(X0,X1)) )
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f6,f11]) ).
fof(f13,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& in_environment(X0,X1) )
=> ( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,sK1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& ~ greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0)))
& in_environment(X0,sK1(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
! [X0] :
( ( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,sK1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& ~ greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0)))
& in_environment(X0,sK1(X0)) )
| ~ stable(X0)
| ~ environment(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f8,f13]) ).
fof(f15,plain,
( ? [X0] :
( ~ in_environment(X0,critical_point(X0))
& stable(X0)
& environment(X0) )
=> ( ~ in_environment(sK2,critical_point(sK2))
& stable(sK2)
& environment(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
( ~ in_environment(sK2,critical_point(sK2))
& stable(sK2)
& environment(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f10,f15]) ).
fof(f17,plain,
! [X0,X1] :
( critical_point(X0) = X1
| subpopulations(first_movers,efficient_producers,X0,sK0(X0,X1))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
! [X0,X1] :
( critical_point(X0) = X1
| greater(sK0(X0,X1),X1)
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0,X1] :
( critical_point(X0) = X1
| ~ greater(growth_rate(efficient_producers,sK0(X0,X1)),growth_rate(first_movers,sK0(X0,X1)))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f20,plain,
! [X0] :
( in_environment(X0,sK1(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f21,plain,
! [X0] :
( ~ greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0)))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f22,plain,
! [X2,X0] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,sK1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f23,plain,
environment(sK2),
inference(cnf_transformation,[],[f16]) ).
fof(f24,plain,
stable(sK2),
inference(cnf_transformation,[],[f16]) ).
fof(f25,plain,
~ in_environment(sK2,critical_point(sK2)),
inference(cnf_transformation,[],[f16]) ).
cnf(c_49,plain,
( ~ greater(growth_rate(efficient_producers,sK0(X0,X1)),growth_rate(first_movers,sK0(X0,X1)))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| critical_point(X0) = X1
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(cnf_transformation,[],[f19]) ).
cnf(c_50,plain,
( ~ in_environment(X0,X1)
| ~ environment(X0)
| critical_point(X0) = X1
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| greater(sK0(X0,X1),X1) ),
inference(cnf_transformation,[],[f18]) ).
cnf(c_51,plain,
( ~ in_environment(X0,X1)
| ~ environment(X0)
| critical_point(X0) = X1
| subpopulations(first_movers,efficient_producers,X0,sK0(X0,X1))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(cnf_transformation,[],[f17]) ).
cnf(c_52,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater(X1,sK1(X0))
| ~ environment(X0)
| ~ stable(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(cnf_transformation,[],[f22]) ).
cnf(c_53,plain,
( ~ greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0)))
| ~ environment(X0)
| ~ stable(X0) ),
inference(cnf_transformation,[],[f21]) ).
cnf(c_54,plain,
( ~ environment(X0)
| ~ stable(X0)
| in_environment(X0,sK1(X0)) ),
inference(cnf_transformation,[],[f20]) ).
cnf(c_55,negated_conjecture,
~ in_environment(sK2,critical_point(sK2)),
inference(cnf_transformation,[],[f25]) ).
cnf(c_56,negated_conjecture,
stable(sK2),
inference(cnf_transformation,[],[f24]) ).
cnf(c_57,negated_conjecture,
environment(sK2),
inference(cnf_transformation,[],[f23]) ).
cnf(c_181,plain,
( sK0(X0,X1) != X2
| X0 != X3
| efficient_producers != efficient_producers
| first_movers != first_movers
| ~ greater(X2,sK1(X3))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ environment(X3)
| ~ stable(X3)
| critical_point(X0) = X1
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(resolution_lifted,[status(thm)],[c_51,c_52]) ).
cnf(c_182,plain,
( ~ greater(sK0(X0,X1),sK1(X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ stable(X0)
| critical_point(X0) = X1
| greater(growth_rate(efficient_producers,sK0(X0,X1)),growth_rate(first_movers,sK0(X0,X1)))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(unflattening,[status(thm)],[c_181]) ).
cnf(c_184,plain,
( critical_point(X0) = X1
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(sK0(X0,X1),sK1(X0))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_182,c_49,c_182]) ).
cnf(c_185,plain,
( ~ greater(sK0(X0,X1),sK1(X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ stable(X0)
| critical_point(X0) = X1
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(renaming,[status(thm)],[c_184]) ).
cnf(c_211,plain,
( X0 != sK2
| ~ greater(sK0(X0,X1),sK1(X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| critical_point(X0) = X1
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(resolution_lifted,[status(thm)],[c_185,c_56]) ).
cnf(c_212,plain,
( ~ greater(sK0(sK2,X0),sK1(sK2))
| ~ in_environment(sK2,X0)
| ~ environment(sK2)
| critical_point(sK2) = X0
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(unflattening,[status(thm)],[c_211]) ).
cnf(c_214,plain,
( ~ in_environment(sK2,X0)
| ~ greater(sK0(sK2,X0),sK1(sK2))
| critical_point(sK2) = X0
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(global_subsumption_just,[status(thm)],[c_212,c_57,c_212]) ).
cnf(c_215,plain,
( ~ greater(sK0(sK2,X0),sK1(sK2))
| ~ in_environment(sK2,X0)
| critical_point(sK2) = X0
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(renaming,[status(thm)],[c_214]) ).
cnf(c_229,plain,
( X0 != sK2
| ~ environment(X0)
| in_environment(X0,sK1(X0)) ),
inference(resolution_lifted,[status(thm)],[c_54,c_56]) ).
cnf(c_230,plain,
( ~ environment(sK2)
| in_environment(sK2,sK1(sK2)) ),
inference(unflattening,[status(thm)],[c_229]) ).
cnf(c_231,plain,
in_environment(sK2,sK1(sK2)),
inference(global_subsumption_just,[status(thm)],[c_230,c_57,c_230]) ).
cnf(c_236,plain,
( X0 != sK2
| ~ greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0)))
| ~ environment(X0) ),
inference(resolution_lifted,[status(thm)],[c_53,c_56]) ).
cnf(c_237,plain,
( ~ greater(growth_rate(efficient_producers,sK1(sK2)),growth_rate(first_movers,sK1(sK2)))
| ~ environment(sK2) ),
inference(unflattening,[status(thm)],[c_236]) ).
cnf(c_249,plain,
( X0 != sK2
| ~ in_environment(X0,X1)
| critical_point(X0) = X1
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| greater(sK0(X0,X1),X1) ),
inference(resolution_lifted,[status(thm)],[c_50,c_57]) ).
cnf(c_250,plain,
( ~ in_environment(sK2,X0)
| critical_point(sK2) = X0
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| greater(sK0(sK2,X0),X0) ),
inference(unflattening,[status(thm)],[c_249]) ).
cnf(c_287,plain,
( critical_point(sK2) != sK1(sK2)
| sK2 != sK2 ),
inference(resolution_lifted,[status(thm)],[c_55,c_231]) ).
cnf(c_304,plain,
( sK1(sK2) != X0
| sK2 != sK2
| critical_point(sK2) = X0
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| greater(sK0(sK2,X0),X0) ),
inference(resolution_lifted,[status(thm)],[c_250,c_231]) ).
cnf(c_305,plain,
( critical_point(sK2) = sK1(sK2)
| greater(growth_rate(efficient_producers,sK1(sK2)),growth_rate(first_movers,sK1(sK2)))
| greater(sK0(sK2,sK1(sK2)),sK1(sK2)) ),
inference(unflattening,[status(thm)],[c_304]) ).
cnf(c_314,plain,
( sK1(sK2) != X0
| sK2 != sK2
| ~ greater(sK0(sK2,X0),sK1(sK2))
| critical_point(sK2) = X0
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(resolution_lifted,[status(thm)],[c_215,c_231]) ).
cnf(c_315,plain,
( ~ greater(sK0(sK2,sK1(sK2)),sK1(sK2))
| critical_point(sK2) = sK1(sK2)
| greater(growth_rate(efficient_producers,sK1(sK2)),growth_rate(first_movers,sK1(sK2))) ),
inference(unflattening,[status(thm)],[c_314]) ).
cnf(c_316,plain,
critical_point(sK2) = sK1(sK2),
inference(global_subsumption_just,[status(thm)],[c_315,c_57,c_237,c_305,c_315]) ).
cnf(c_321,plain,
sK2 != sK2,
inference(backward_subsumption_resolution,[status(thm)],[c_287,c_316]) ).
cnf(c_324,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_321]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : MGT023+1 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.14/0.36 % Computer : n027.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Mon Aug 28 06:44:22 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.20/0.49 Running first-order theorem proving
% 0.20/0.49 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.80/1.20 % SZS status Started for theBenchmark.p
% 0.80/1.20 % SZS status Theorem for theBenchmark.p
% 0.80/1.20
% 0.80/1.20 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.80/1.20
% 0.80/1.20 ------ iProver source info
% 0.80/1.20
% 0.80/1.20 git: date: 2023-05-31 18:12:56 +0000
% 0.80/1.20 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.80/1.20 git: non_committed_changes: false
% 0.80/1.20 git: last_make_outside_of_git: false
% 0.80/1.20
% 0.80/1.20 ------ Parsing...
% 0.80/1.20 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.80/1.20
% 0.80/1.20 ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e
% 0.80/1.20
% 0.80/1.20 % SZS status Theorem for theBenchmark.p
% 0.80/1.20
% 0.80/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.80/1.20
% 0.80/1.20
%------------------------------------------------------------------------------