%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT032-2 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n010.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 02:12:26 PM UTC 2026
% Result : Unsatisfiable 1.22s 6.72s
% Output : CNFRefutation 1.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 8
% Syntax : Number of formulae : 22 ( 5 unt; 0 def)
% Number of atoms : 60 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 81 ( 43 ~; 38 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 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 : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 24 ( 0 sgn 24 !; 0 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] :
( selection_favors(X2,X1,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates_1) ).
fof(f2,axiom,
! [X0] :
( in_environment(X0,sk1(X0))
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_2) ).
fof(f3,axiom,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ greater_or_equal(X1,sk1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1_3) ).
fof(f4,negated_conjecture,
environment(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t1_4) ).
fof(f5,negated_conjecture,
stable(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t1_5) ).
fof(f6,negated_conjecture,
! [X0] :
( subpopulations(first_movers,efficient_producers,sk2,sk3(X0))
| ~ in_environment(sk2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t1_6) ).
fof(f7,negated_conjecture,
! [X0] :
( greater_or_equal(sk3(X0),X0)
| ~ in_environment(sk2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t1_7) ).
fof(f8,negated_conjecture,
! [X0] :
( ~ selection_favors(efficient_producers,first_movers,sk3(X0))
| ~ in_environment(sk2,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t1_8) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( selection_favors(X0,X2,X1)
| ~ environment(X3)
| ~ subpopulations(X2,X0,X3,X1)
| ~ greater(growth_rate(X0,X1),growth_rate(X2,X1)) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_58,plain,
! [X0: $i] :
( in_environment(X0,sk1(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),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,[],[f3]) ).
tcf(c_60,negated_conjecture,
environment(sk2),
inference(cnf_transformation,[],[f4]) ).
tcf(c_61,negated_conjecture,
stable(sk2),
inference(cnf_transformation,[],[f5]) ).
tcf(c_62,negated_conjecture,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sk2,sk3(X0))
| ~ in_environment(sk2,X0) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_63,negated_conjecture,
! [X0: $i] :
( greater_or_equal(sk3(X0),X0)
| ~ in_environment(sk2,X0) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_64,negated_conjecture,
! [X0: $i] :
( ~ in_environment(sk2,X0)
| ~ selection_favors(efficient_producers,first_movers,sk3(X0)) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_68,plain,
( in_environment(sk2,sk1(sk2))
| ~ stable(sk2)
| ~ environment(sk2) ),
inference(instantiation,[status(thm)],[c_58]) ).
tcf(c_111,plain,
! [X0: $i,X1: $i] :
( ~ environment(X1)
| ~ in_environment(sk2,X0)
| ~ subpopulations(first_movers,efficient_producers,X1,sk3(X0))
| ~ greater(growth_rate(efficient_producers,sk3(X0)),growth_rate(first_movers,sk3(X0))) ),
inference(resolution,[status(thm)],[c_57,c_64]) ).
tcf(c_129,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,sk3(sk1(X0))),growth_rate(first_movers,sk3(sk1(X0))))
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(sk2,sk1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,sk3(sk1(X0))) ),
inference(resolution,[status(thm)],[c_59,c_63]) ).
tcf(c_141,plain,
! [X0: $i] :
( ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(sk2,sk1(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,sk3(sk1(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_129,c_111]) ).
tcf(c_151,plain,
( ~ stable(sk2)
| ~ environment(sk2)
| ~ in_environment(sk2,sk1(sk2)) ),
inference(resolution,[status(thm)],[c_62,c_141]) ).
tcf(c_152,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_151,c_68,c_60,c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT032-2 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/5.81 % Computer : n010.cluster.edu
% 0.12/5.81 % Model : x86_64 x86_64
% 0.12/5.81 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.81 % Memory : 8046.5625MB
% 0.12/5.81 % OS : Linux 6.8.0-71-generic
% 0.12/5.81 % CPULimit : 300
% 0.12/5.81 % WCLimit : 300
% 0.12/5.81 % DateTime : Thu Sep 24 01:06:36 UTC 2026
% 0.12/5.81 % CPUTime :
% 0.12/5.81 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/5.85 Running first-order theorem proving
% 0.12/5.85 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
% 0.12/5.86
% 0.12/5.86 % ======== iProver multi-core TPTP/SMT =========
% 0.12/5.86
% 0.12/5.86 % Detected problem language: tptp
% 0.12/5.87 % Proving...
% 1.22/6.72 % SZS status Started for theBenchmark.p
% 1.22/6.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.22/6.72
% 1.22/6.72 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.22/6.72
% 1.22/6.72 % ------ iProver source info
% 1.22/6.72
% 1.22/6.72 % git: date: 2026-07-19 20:42:38 +0200
% 1.22/6.72 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.22/6.72 % git: non_committed_changes: false
% 1.22/6.72
% 1.22/6.72 % ------ Parsing...% successful
% 1.22/6.72
% 1.22/6.72
% 1.22/6.72 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.22/6.72
% 1.22/6.72 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s%
% 1.22/6.72
% 1.22/6.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.22/6.72
% 1.22/6.72 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.22/6.72
% 1.22/6.72
%------------------------------------------------------------------------------