%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT023-1 : 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 : n020.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 : Unsatisfiable 1.26s 16.32s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 10 unt; 0 def)
% Number of atoms : 164 ( 39 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 213 ( 93 ~; 120 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 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 : 48 ( 0 sgn 48 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( X1 = critical_point(X0)
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_17) ).
fof(f2,plain,
! [X0,X1] :
( critical_point(X0) = X1
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(reorient_equations,[],[f1]) ).
fof(f3,axiom,
! [X0,X1] :
( X1 = critical_point(X0)
| greater(sk1(X1,X0),X1)
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_18) ).
fof(f4,plain,
! [X0,X1] :
( critical_point(X0) = X1
| greater(sk1(X1,X0),X1)
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0,X1] :
( X1 = critical_point(X0)
| ~ greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0)))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_19) ).
fof(f6,plain,
! [X0,X1] :
( critical_point(X0) = X1
| ~ greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0)))
| ~ in_environment(X0,X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0) ),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X0] :
( in_environment(X0,sk2(X0))
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_20) ).
fof(f8,axiom,
! [X0] :
( ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0)))
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_21) ).
fof(f9,axiom,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater(X1,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_22) ).
fof(f10,negated_conjecture,
environment(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_23) ).
fof(f11,negated_conjecture,
stable(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_24) ).
fof(f12,negated_conjecture,
~ in_environment(sk3,critical_point(sk3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_25) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ( critical_point(X0) = X1 )
| ~ environment(X0)
| ~ in_environment(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( greater(sk1(X1,X0),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,[],[f4]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(X1) = X0 )
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(growth_rate(efficient_producers,sk1(X0,X1)),growth_rate(first_movers,sk1(X0,X1))) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_61,plain,
! [X0: $i] :
( in_environment(X0,sk2(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_62,plain,
! [X0: $i] :
( ~ stable(X0)
| ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0))) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ stable(X0)
| ~ environment(X0)
| ~ greater(X1,sk2(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_64,negated_conjecture,
environment(sk3),
inference(cnf_transformation,[],[f10]) ).
tcf(c_65,negated_conjecture,
stable(sk3),
inference(cnf_transformation,[],[f11]) ).
tcf(c_66,negated_conjecture,
~ in_environment(sk3,critical_point(sk3)),
inference(cnf_transformation,[],[f12]) ).
tcf(c_190,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,X0),growth_rate(first_movers,X0))
| ( critical_point(X1) = X0 )
| ~ stable(X3)
| ~ environment(X3)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(X2,sk2(X3))
| ( first_movers != first_movers )
| ( efficient_producers != efficient_producers )
| ( X1 != X3 )
| ( sk1(X0,X1) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_63]) ).
tcf(c_191,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| greater(growth_rate(efficient_producers,sk1(X0,X1)),growth_rate(first_movers,sk1(X0,X1)))
| ( critical_point(X1) = X0 )
| ~ stable(X1)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(sk1(X0,X1),sk2(X1)) ),
inference(unflattening,[status(thm)],[c_190]) ).
tcf(c_193,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(sk1(X0,X1),sk2(X1))
| ~ in_environment(X1,X0)
| ~ environment(X1)
| ~ stable(X1)
| ( critical_point(X1) = X0 ) ),
inference(global_subsumption_just,[status(thm)],[c_191,c_60,c_191]) ).
tcf(c_194,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(X1) = X0 )
| ~ stable(X1)
| ~ environment(X1)
| ~ in_environment(X1,X0)
| ~ greater(sk1(X0,X1),sk2(X1)) ),
inference(renaming,[status(thm)],[c_193]) ).
tcf(c_220,plain,
! [X0: $i] :
( ~ environment(X0)
| ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0)))
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_62,c_65]) ).
tcf(c_221,plain,
( ~ environment(sk3)
| ~ greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) ),
inference(unflattening,[status(thm)],[c_220]) ).
tcf(c_227,plain,
! [X0: $i] :
( in_environment(X0,sk2(X0))
| ~ environment(X0)
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_61,c_65]) ).
tcf(c_228,plain,
( in_environment(sk3,sk2(sk3))
| ~ environment(sk3) ),
inference(unflattening,[status(thm)],[c_227]) ).
tcf(c_229,plain,
in_environment(sk3,sk2(sk3)),
inference(global_subsumption_just,[status(thm)],[c_228,c_64,c_228]) ).
tcf(c_234,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(sk1(X1,X0),sk2(X0))
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_65,c_194]) ).
tcf(c_235,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(sk3) = X0 )
| ~ environment(sk3)
| ~ in_environment(sk3,X0)
| ~ greater(sk1(X0,sk3),sk2(sk3)) ),
inference(unflattening,[status(thm)],[c_234]) ).
tcf(c_237,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(sk3) = X0 )
| ~ greater(sk1(X0,sk3),sk2(sk3))
| ~ in_environment(sk3,X0) ),
inference(global_subsumption_just,[status(thm)],[c_235,c_64,c_235]) ).
tcf(c_238,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(sk3) = X0 )
| ~ in_environment(sk3,X0)
| ~ greater(sk1(X0,sk3),sk2(sk3)) ),
inference(renaming,[status(thm)],[c_237]) ).
tcf(c_258,plain,
! [X0: $i,X1: $i] :
( greater(sk1(X1,X0),X1)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ( critical_point(X0) = X1 )
| ~ in_environment(X0,X1)
| ( X0 != sk3 ) ),
inference(resolution_lifted,[status(thm)],[c_59,c_64]) ).
tcf(c_259,plain,
! [X0: $i] :
( greater(sk1(X0,sk3),X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(sk3) = X0 )
| ~ in_environment(sk3,X0) ),
inference(unflattening,[status(thm)],[c_258]) ).
tcf(c_296,plain,
( ( sk3 != sk3 )
| ( critical_point(sk3) != sk2(sk3) ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_229]) ).
tcf(c_313,plain,
! [X0: $i] :
( greater(sk1(X0,sk3),X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(sk3) = X0 )
| ( sk3 != sk3 )
| ( sk2(sk3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_229,c_259]) ).
tcf(c_314,plain,
( greater(sk1(sk2(sk3),sk3),sk2(sk3))
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3)))
| ( critical_point(sk3) = sk2(sk3) ) ),
inference(unflattening,[status(thm)],[c_313]) ).
tcf(c_323,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ( critical_point(sk3) = X0 )
| ~ greater(sk1(X0,sk3),sk2(sk3))
| ( sk3 != sk3 )
| ( sk2(sk3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_229,c_238]) ).
tcf(c_324,plain,
( greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3)))
| ( critical_point(sk3) = sk2(sk3) )
| ~ greater(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(unflattening,[status(thm)],[c_323]) ).
tcf(c_325,plain,
critical_point(sk3) = sk2(sk3),
inference(global_subsumption_just,[status(thm)],[c_324,c_64,c_221,c_314,c_324]) ).
tcf(c_330,plain,
sk3 != sk3,
inference(backward_subsumption_resolution,[status(thm)],[c_296,c_325]) ).
tcf(c_333,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_330]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT023-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/15.40 % Computer : n020.cluster.edu
% 0.12/15.40 % Model : x86_64 x86_64
% 0.12/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/15.40 % Memory : 8046.5625MB
% 0.12/15.40 % OS : Linux 6.8.0-71-generic
% 0.12/15.40 % CPULimit : 300
% 0.12/15.40 % WCLimit : 300
% 0.12/15.40 % DateTime : Thu Sep 24 01:04:20 UTC 2026
% 0.12/15.41 % CPUTime :
% 0.12/15.41 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/15.44 Running first-order theorem proving
% 0.12/15.44 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
% 0.12/15.46
% 0.12/15.46 % ======== iProver multi-core TPTP/SMT =========
% 0.12/15.46
% 0.12/15.46 % Detected problem language: tptp
% 0.12/15.47 % Proving...
% 1.26/16.32 % SZS status Started for theBenchmark.p
% 1.26/16.32 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/16.32
% 1.26/16.32 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.26/16.32
% 1.26/16.32 % ------ iProver source info
% 1.26/16.32
% 1.26/16.32 % git: date: 2026-07-19 20:42:38 +0200
% 1.26/16.32 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.26/16.32 % git: non_committed_changes: false
% 1.26/16.32
% 1.26/16.32 % ------ Parsing...% successful
% 1.26/16.32
% 1.26/16.32
% 1.26/16.32 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.26/16.32
% 1.26/16.32 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e %
% 1.26/16.32
% 1.26/16.32 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/16.32
% 1.26/16.32 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.26/16.32
% 1.26/16.32
%------------------------------------------------------------------------------