%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT023+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:12:23 PM UTC 2026
% Result : Theorem 1.26s 1.28s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 54 ( 10 unt; 0 def)
% Number of atoms : 220 ( 40 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 282 ( 116 ~; 132 |; 28 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 68 ( 0 sgn 61 !; 7 ?; 32 :)
% 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) )
=> X1 = critical_point(X0) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',l12) ).
fof(f3,conjecture,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> in_environment(X0,critical_point(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l5) ).
fof(f4,negated_conjecture,
~ ! [X0] :
( ( stable(X0)
& environment(X0) )
=> in_environment(X0,critical_point(X0)) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [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)
| X1 = critical_point(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f6,plain,
! [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)
| X1 = critical_point(X0) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [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) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f8,plain,
! [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) ) ),
inference(flattening,[],[f7]) ).
fof(f9,plain,
? [X0] :
( stable(X0)
& environment(X0)
& ~ in_environment(X0,critical_point(X0)) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,plain,
? [X0] :
( stable(X0)
& environment(X0)
& ~ in_environment(X0,critical_point(X0)) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ( greater(sK0(X0,X1),X1)
& subpopulations(first_movers,efficient_producers,X0,sK0(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)
| X1 = critical_point(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f6]) ).
fof(f12,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| ( ! [X2] :
( ~ greater(X2,sK1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& ~ greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0)))
& in_environment(X0,sK1(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f8]) ).
fof(f13,plain,
( stable(sK2)
& environment(sK2)
& ~ in_environment(sK2,critical_point(sK2)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f10]) ).
fof(f14,plain,
! [X0,X1] :
( greater(sK0(X0,X1),X1)
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0)
| critical_point(X0) = X1 ),
inference(cnf_transformation,[],[f11]) ).
fof(f15,plain,
! [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)
| critical_point(X0) = X1 ),
inference(cnf_transformation,[],[f11]) ).
fof(f16,plain,
! [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)
| critical_point(X0) = X1 ),
inference(cnf_transformation,[],[f11]) ).
fof(f17,plain,
! [X2,X0] :
( ~ stable(X0)
| ~ environment(X0)
| ~ greater(X2,sK1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0))) ),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| in_environment(X0,sK1(X0)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f20,plain,
stable(sK2),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
environment(sK2),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
~ in_environment(sK2,critical_point(sK2)),
inference(cnf_transformation,[],[f13]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ( critical_point(X0) = X1 )
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(growth_rate(efficient_producers,sK0(X0,X1)),growth_rate(first_movers,sK0(X0,X1))) ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| subpopulations(first_movers,efficient_producers,X0,sK0(X0,X1))
| ( critical_point(X0) = X1 )
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( greater(sK0(X0,X1),X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ( critical_point(X0) = X1 )
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_52,plain,
! [X0: $i] :
( in_environment(X0,sK1(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_53,plain,
! [X0: $i] :
( ~ stable(X0)
| ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0))) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ stable(X0)
| ~ environment(X0)
| ~ greater(X1,sK1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
tcf(c_55,negated_conjecture,
~ in_environment(sK2,critical_point(sK2)),
inference(cnf_transformation,[],[f22]) ).
tcf(c_56,negated_conjecture,
environment(sK2),
inference(cnf_transformation,[],[f21]) ).
tcf(c_57,negated_conjecture,
stable(sK2),
inference(cnf_transformation,[],[f20]) ).
tcf(c_181,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ( critical_point(X0) = X1 )
| ~ stable(X3)
| ~ environment(X3)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(X2,sK1(X3))
| ( first_movers != first_movers )
| ( efficient_producers != efficient_producers )
| ( X0 != X3 )
| ( sK0(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_54]) ).
tcf(c_182,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| greater(growth_rate(efficient_producers,sK0(X0,X1)),growth_rate(first_movers,sK0(X0,X1)))
| ( critical_point(X0) = X1 )
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(sK0(X0,X1),sK1(X0)) ),
inference(unflattening,[status(thm)],[c_181]) ).
tcf(c_184,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(sK0(X0,X1),sK1(X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ stable(X0)
| ( critical_point(X0) = X1 ) ),
inference(global_subsumption_just,[status(thm)],[c_182,c_49,c_182]) ).
tcf(c_185,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ( critical_point(X0) = X1 )
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(sK0(X0,X1),sK1(X0)) ),
inference(renaming,[status(thm)],[c_184]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ( critical_point(X0) = X1 )
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(sK0(X0,X1),sK1(X0))
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_185,c_57]) ).
tcf(c_212,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(sK2) = X0 )
| ~ environment(sK2)
| ~ in_environment(sK2,X0)
| ~ greater(sK0(sK2,X0),sK1(sK2)) ),
inference(unflattening,[status(thm)],[c_211]) ).
tcf(c_214,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(sK2) = X0 )
| ~ greater(sK0(sK2,X0),sK1(sK2))
| ~ in_environment(sK2,X0) ),
inference(global_subsumption_just,[status(thm)],[c_212,c_56,c_212]) ).
tcf(c_215,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(sK2) = X0 )
| ~ in_environment(sK2,X0)
| ~ greater(sK0(sK2,X0),sK1(sK2)) ),
inference(renaming,[status(thm)],[c_214]) ).
tcf(c_229,plain,
! [X0: $i] :
( ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0)))
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_57]) ).
tcf(c_230,plain,
( ~ environment(sK2)
| ~ greater(growth_rate(efficient_producers,sK1(sK2)),growth_rate(first_movers,sK1(sK2))) ),
inference(unflattening,[status(thm)],[c_229]) ).
tcf(c_236,plain,
! [X0: $i] :
( in_environment(X0,sK1(X0))
| ~ environment(X0)
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_57]) ).
tcf(c_237,plain,
( in_environment(sK2,sK1(sK2))
| ~ environment(sK2) ),
inference(unflattening,[status(thm)],[c_236]) ).
tcf(c_238,plain,
in_environment(sK2,sK1(sK2)),
inference(global_subsumption_just,[status(thm)],[c_237,c_56,c_237]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i] :
( greater(sK0(X0,X1),X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ( critical_point(X0) = X1 )
| ~ in_environment(X0,X1)
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_56]) ).
tcf(c_250,plain,
! [X0: $i] :
( greater(sK0(sK2,X0),X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(sK2) = X0 )
| ~ in_environment(sK2,X0) ),
inference(unflattening,[status(thm)],[c_249]) ).
tcf(c_287,plain,
( ( sK2 != sK2 )
| ( critical_point(sK2) != sK1(sK2) ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_238]) ).
tcf(c_304,plain,
! [X0: $i] :
( greater(sK0(sK2,X0),X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(sK2) = X0 )
| ( sK2 != sK2 )
| ( sK1(sK2) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_250,c_238]) ).
tcf(c_305,plain,
( greater(sK0(sK2,sK1(sK2)),sK1(sK2))
| greater(growth_rate(efficient_producers,sK1(sK2)),growth_rate(first_movers,sK1(sK2)))
| ( critical_point(sK2) = sK1(sK2) ) ),
inference(unflattening,[status(thm)],[c_304]) ).
tcf(c_314,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(sK2) = X0 )
| ~ greater(sK0(sK2,X0),sK1(sK2))
| ( sK2 != sK2 )
| ( sK1(sK2) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_215,c_238]) ).
tcf(c_315,plain,
( greater(growth_rate(efficient_producers,sK1(sK2)),growth_rate(first_movers,sK1(sK2)))
| ( critical_point(sK2) = sK1(sK2) )
| ~ greater(sK0(sK2,sK1(sK2)),sK1(sK2)) ),
inference(unflattening,[status(thm)],[c_314]) ).
tcf(c_316,plain,
critical_point(sK2) = sK1(sK2),
inference(global_subsumption_just,[status(thm)],[c_315,c_56,c_230,c_305,c_315]) ).
tcf(c_321,plain,
sK2 != sK2,
inference(backward_subsumption_resolution,[status(thm)],[c_287,c_316]) ).
tcf(c_324,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_321]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT023+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n001.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 01:08:06 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 1.26/1.28 % SZS status Started for theBenchmark.p
% 1.26/1.28 % SZS status Theorem for theBenchmark.p
% 1.26/1.28
% 1.26/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.26/1.28
% 1.26/1.28 % ------ iProver source info
% 1.26/1.28
% 1.26/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.26/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.26/1.28 % git: non_committed_changes: false
% 1.26/1.28
% 1.26/1.28 % ------ Parsing...
% 1.26/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.26/1.28
% 1.26/1.28 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e %
% 1.26/1.28
% 1.26/1.28 % SZS status Theorem for theBenchmark.p
% 1.26/1.28
% 1.26/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.26/1.28
% 1.26/1.28
%------------------------------------------------------------------------------