%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT032+2 : 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 : n004.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 : Theorem 1.23s 1.51s
% Output : CNFRefutation 1.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 5 unt; 0 def)
% Number of atoms : 126 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 160 ( 68 ~; 59 |; 26 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 60 ( 0 sgn 51 !; 9 ?; 14 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2,X3] :
( ( greater(growth_rate(X2,X3),growth_rate(X1,X3))
& subpopulations(X1,X2,X0,X3)
& environment(X0) )
=> selection_favors(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
fof(f2,axiom,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( ! [X2] :
( ( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& in_environment(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).
fof(f3,conjecture,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( ! [X2] :
( ( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> selection_favors(efficient_producers,first_movers,X2) )
& in_environment(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t1) ).
fof(f4,negated_conjecture,
~ ! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X1] :
( ! [X2] :
( ( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
=> selection_favors(efficient_producers,first_movers,X2) )
& in_environment(X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [X0,X1,X2,X3] :
( ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| selection_favors(X2,X1,X3) ),
inference(ennf_transformation,[],[f1]) ).
fof(f6,plain,
! [X0,X1,X2,X3] :
( ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| selection_favors(X2,X1,X3) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| ? [X1] :
( ! [X2] :
( ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& in_environment(X0,X1) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f8,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| ? [X1] :
( ! [X2] :
( ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& in_environment(X0,X1) ) ),
inference(flattening,[],[f7]) ).
fof(f9,plain,
? [X0] :
( stable(X0)
& environment(X0)
& ! [X1] :
( ? [X2] :
( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2)
& ~ selection_favors(efficient_producers,first_movers,X2) )
| ~ in_environment(X0,X1) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,plain,
? [X0] :
( stable(X0)
& environment(X0)
& ! [X1] :
( ? [X2] :
( greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2)
& ~ selection_favors(efficient_producers,first_movers,X2) )
| ~ in_environment(X0,X1) ) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| ( ! [X2] :
( ~ greater_or_equal(X2,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) )
& in_environment(X0,sK0(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f8]) ).
fof(f12,plain,
( stable(sK1)
& environment(sK1)
& ! [X1] :
( ( greater_or_equal(sK2(X1),X1)
& subpopulations(first_movers,efficient_producers,sK1,sK2(X1))
& ~ selection_favors(efficient_producers,first_movers,sK2(X1)) )
| ~ in_environment(sK1,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X2,sK2(X1))],[f10]) ).
fof(f13,plain,
! [X2,X3,X0,X1] :
( ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| selection_favors(X2,X1,X3) ),
inference(cnf_transformation,[],[f6]) ).
fof(f14,plain,
! [X2,X0] :
( ~ stable(X0)
| ~ environment(X0)
| ~ greater_or_equal(X2,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f15,plain,
! [X0] :
( ~ stable(X0)
| ~ environment(X0)
| in_environment(X0,sK0(X0)) ),
inference(cnf_transformation,[],[f11]) ).
fof(f16,plain,
stable(sK1),
inference(cnf_transformation,[],[f12]) ).
fof(f17,plain,
environment(sK1),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
! [X1] :
( greater_or_equal(sK2(X1),X1)
| ~ in_environment(sK1,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X1] :
( subpopulations(first_movers,efficient_producers,sK1,sK2(X1))
| ~ in_environment(sK1,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f20,plain,
! [X1] :
( ~ selection_favors(efficient_producers,first_movers,sK2(X1))
| ~ in_environment(sK1,X1) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_49,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,[],[f13]) ).
tcf(c_50,plain,
! [X0: $i] :
( in_environment(X0,sK0(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ stable(X0)
| ~ environment(X0)
| ~ greater_or_equal(X1,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_52,negated_conjecture,
! [X0: $i] :
( ~ in_environment(sK1,X0)
| ~ selection_favors(efficient_producers,first_movers,sK2(X0)) ),
inference(cnf_transformation,[],[f20]) ).
tcf(c_53,negated_conjecture,
! [X0: $i] :
( subpopulations(first_movers,efficient_producers,sK1,sK2(X0))
| ~ in_environment(sK1,X0) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_54,negated_conjecture,
! [X0: $i] :
( greater_or_equal(sK2(X0),X0)
| ~ in_environment(sK1,X0) ),
inference(cnf_transformation,[],[f18]) ).
tcf(c_55,negated_conjecture,
environment(sK1),
inference(cnf_transformation,[],[f17]) ).
tcf(c_56,negated_conjecture,
stable(sK1),
inference(cnf_transformation,[],[f16]) ).
tcf(c_60,plain,
( in_environment(sK1,sK0(sK1))
| ~ stable(sK1)
| ~ environment(sK1) ),
inference(instantiation,[status(thm)],[c_50]) ).
tcf(c_103,plain,
! [X0: $i,X1: $i] :
( ~ environment(X1)
| ~ in_environment(sK1,X0)
| ~ subpopulations(first_movers,efficient_producers,X1,sK2(X0))
| ~ greater(growth_rate(efficient_producers,sK2(X0)),growth_rate(first_movers,sK2(X0))) ),
inference(resolution,[status(thm)],[c_49,c_52]) ).
tcf(c_121,plain,
! [X0: $i] :
( greater(growth_rate(efficient_producers,sK2(sK0(X0))),growth_rate(first_movers,sK2(sK0(X0))))
| ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(sK1,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,sK2(sK0(X0))) ),
inference(resolution,[status(thm)],[c_51,c_54]) ).
tcf(c_133,plain,
! [X0: $i] :
( ~ stable(X0)
| ~ environment(X0)
| ~ in_environment(sK1,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,sK2(sK0(X0))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_121,c_103]) ).
tcf(c_143,plain,
( ~ stable(sK1)
| ~ environment(sK1)
| ~ in_environment(sK1,sK0(sK1)) ),
inference(resolution,[status(thm)],[c_53,c_133]) ).
tcf(c_144,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_143,c_60,c_55,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT032+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.59 % Computer : n004.cluster.edu
% 0.10/0.59 % Model : x86_64 x86_64
% 0.10/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.59 % Memory : 8046.5625MB
% 0.10/0.59 % OS : Linux 6.8.0-71-generic
% 0.10/0.59 % CPULimit : 300
% 0.10/0.59 % WCLimit : 300
% 0.10/0.59 % DateTime : Thu Sep 24 01:05:53 UTC 2026
% 0.10/0.59 % CPUTime :
% 0.10/0.59 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.63 Running first-order theorem proving
% 0.10/0.63 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
% 0.16/0.64
% 0.16/0.64 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.64
% 0.16/0.64 % Detected problem language: tptp
% 0.16/0.65 % Proving...
% 1.23/1.51 % SZS status Started for theBenchmark.p
% 1.23/1.51 % SZS status Theorem for theBenchmark.p
% 1.23/1.51
% 1.23/1.51 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.23/1.51
% 1.23/1.51 % ------ iProver source info
% 1.23/1.51
% 1.23/1.51 % git: date: 2026-07-19 20:42:38 +0200
% 1.23/1.51 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.23/1.51 % git: non_committed_changes: false
% 1.23/1.51
% 1.23/1.51 % ------ Parsing...
% 1.23/1.51 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.23/1.51
% 1.23/1.51 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s%
% 1.23/1.51
% 1.23/1.51 % SZS status Theorem for theBenchmark.p
% 1.23/1.51
% 1.23/1.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.23/1.51
% 1.23/1.51
%------------------------------------------------------------------------------