%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : MGT036+3 : 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 : n018.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 02:12:31 PM UTC 2026
% Result : Theorem 1.61s 6.28s
% Output : CNFRefutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 11 unt; 0 def)
% Number of atoms : 109 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 128 ( 56 ~; 48 |; 19 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 3 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 66 !; 6 ?; 22 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2,X3] :
( ( subpopulations(X1,X2,X0,X3)
& environment(X0) )
=> subpopulations(X2,X1,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
fof(f2,axiom,
! [X0,X1,X2,X3] :
( ( subpopulations(X1,X2,X0,X3)
& environment(X0) )
=> ( ( greater(zero,growth_rate(X1,X3))
& greater_or_equal(growth_rate(X2,X3),zero) )
<=> outcompetes(X2,X1,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
fof(f3,axiom,
? [X0,X1] :
( greater(zero,growth_rate(efficient_producers,X1))
& greater_or_equal(growth_rate(first_movers,X1),zero)
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star) ).
fof(f4,conjecture,
? [X0,X1] :
( outcompetes(first_movers,efficient_producers,X1)
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5_star) ).
fof(f5,negated_conjecture,
~ ? [X0,X1] :
( outcompetes(first_movers,efficient_producers,X1)
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) ),
inference(negated_conjecture,[status(cth)],[f4]) ).
fof(f6,plain,
! [X0,X1,X2,X3] :
( ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| subpopulations(X2,X1,X0,X3) ),
inference(ennf_transformation,[],[f1]) ).
fof(f7,plain,
! [X0,X1,X2,X3] :
( ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| subpopulations(X2,X1,X0,X3) ),
inference(flattening,[],[f6]) ).
fof(f8,plain,
! [X0,X1,X2,X3] :
( ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| ( ( greater(zero,growth_rate(X1,X3))
& greater_or_equal(growth_rate(X2,X3),zero) )
<=> outcompetes(X2,X1,X3) ) ),
inference(ennf_transformation,[],[f2]) ).
fof(f9,plain,
! [X0,X1,X2,X3] :
( ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| ( ( greater(zero,growth_rate(X1,X3))
& greater_or_equal(growth_rate(X2,X3),zero) )
<=> outcompetes(X2,X1,X3) ) ),
inference(flattening,[],[f8]) ).
fof(f10,plain,
! [X0,X1] :
( ~ outcompetes(first_movers,efficient_producers,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f11,plain,
! [X0,X1,X2,X3] :
( ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| ( ( ~ greater(zero,growth_rate(X1,X3))
| ~ greater_or_equal(growth_rate(X2,X3),zero)
| outcompetes(X2,X1,X3) )
& ( ~ outcompetes(X2,X1,X3)
| ( greater(zero,growth_rate(X1,X3))
& greater_or_equal(growth_rate(X2,X3),zero) ) ) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f12,plain,
! [X0,X1,X2,X3] :
( ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| ( ( ~ greater(zero,growth_rate(X1,X3))
| ~ greater_or_equal(growth_rate(X2,X3),zero)
| outcompetes(X2,X1,X3) )
& ( ~ outcompetes(X2,X1,X3)
| ( greater(zero,growth_rate(X1,X3))
& greater_or_equal(growth_rate(X2,X3),zero) ) ) ) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
( greater(zero,growth_rate(efficient_producers,sK1))
& greater_or_equal(growth_rate(first_movers,sK1),zero)
& subpopulations(first_movers,efficient_producers,sK0,sK1)
& environment(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f3]) ).
fof(f14,plain,
! [X2,X3,X0,X1] :
( ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| subpopulations(X2,X1,X0,X3) ),
inference(cnf_transformation,[],[f7]) ).
fof(f15,plain,
! [X2,X3,X0,X1] :
( ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| ~ greater(zero,growth_rate(X1,X3))
| ~ greater_or_equal(growth_rate(X2,X3),zero)
| outcompetes(X2,X1,X3) ),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
greater(zero,growth_rate(efficient_producers,sK1)),
inference(cnf_transformation,[],[f13]) ).
fof(f19,plain,
greater_or_equal(growth_rate(first_movers,sK1),zero),
inference(cnf_transformation,[],[f13]) ).
fof(f20,plain,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
environment(sK0),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
! [X0,X1] :
( ~ outcompetes(first_movers,efficient_producers,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( subpopulations(X1,X0,X2,X3)
| ~ environment(X2)
| ~ subpopulations(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f14]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( outcompetes(X1,X0,X3)
| ~ environment(X2)
| ~ greater(zero,growth_rate(X0,X3))
| ~ greater_or_equal(growth_rate(X1,X3),zero)
| ~ subpopulations(X0,X1,X2,X3) ),
inference(cnf_transformation,[],[f15]) ).
tcf(c_53,plain,
environment(sK0),
inference(cnf_transformation,[],[f21]) ).
tcf(c_54,plain,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f20]) ).
tcf(c_55,plain,
greater_or_equal(growth_rate(first_movers,sK1),zero),
inference(cnf_transformation,[],[f19]) ).
tcf(c_56,plain,
greater(zero,growth_rate(efficient_producers,sK1)),
inference(cnf_transformation,[],[f18]) ).
tcf(c_57,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ environment(X0)
| ~ outcompetes(first_movers,efficient_producers,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_202,plain,
! [X0: $i,X1: $i,X2: $i] :
( outcompetes(X1,X0,X2)
| ~ greater(zero,growth_rate(X0,X2))
| ~ greater_or_equal(growth_rate(X1,X2),zero)
| ~ subpopulations(X0,X1,sK0,X2) ),
inference(resolution,[status(thm)],[c_52,c_53]) ).
tcf(c_238,plain,
! [X0: $i,X1: $i,X2: $i] :
( subpopulations(X1,X0,sK0,X2)
| ~ subpopulations(X0,X1,sK0,X2) ),
inference(resolution,[status(thm)],[c_49,c_53]) ).
tcf(c_245,plain,
! [X0: $i] :
( ~ outcompetes(first_movers,efficient_producers,X0)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(resolution,[status(thm)],[c_53,c_57]) ).
tcf(c_339,plain,
! [X0: $i] :
( ~ greater(zero,growth_rate(efficient_producers,X0))
| ~ greater_or_equal(growth_rate(first_movers,X0),zero)
| ~ subpopulations(efficient_producers,first_movers,sK0,X0)
| ~ subpopulations(first_movers,efficient_producers,sK0,X0) ),
inference(resolution,[status(thm)],[c_202,c_245]) ).
tcf(c_349,plain,
! [X0: $i] :
( ~ greater(zero,growth_rate(efficient_producers,X0))
| ~ greater_or_equal(growth_rate(first_movers,X0),zero)
| ~ subpopulations(efficient_producers,first_movers,sK0,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_339,c_238]) ).
tcf(c_357,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK1))
| ~ subpopulations(efficient_producers,first_movers,sK0,sK1) ),
inference(resolution,[status(thm)],[c_55,c_349]) ).
tcf(c_373,plain,
! [X0_iProver_subpopulations_2: iProver_subpopulations_2,X0_iProver_subpopulations_4: iProver_subpopulations_4,X1_iProver_subpopulations_2: iProver_subpopulations_2] :
( subpopulations(X1_iProver_subpopulations_2,X0_iProver_subpopulations_2,sK0,X0_iProver_subpopulations_4)
| ~ subpopulations(X0_iProver_subpopulations_2,X1_iProver_subpopulations_2,sK0,X0_iProver_subpopulations_4) ),
inference(subtyping,[status(esa)],[c_238]) ).
tcf(c_374,plain,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(subtyping,[status(esa)],[c_54]) ).
tcf(c_376,plain,
subpopulations(efficient_producers,first_movers,sK0,sK1),
inference(resolution,[status(thm)],[c_373,c_374]) ).
tcf(c_377,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_376,c_357,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT036+3 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/5.37 % Computer : n018.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Thu Sep 24 01:10:39 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/5.41 Running first-order theorem proving
% 0.13/5.41 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
% 0.13/5.42
% 0.13/5.42 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.42
% 0.13/5.42 % Detected problem language: tptp
% 0.13/5.43 % Proving...
% 1.61/6.28 % SZS status Started for theBenchmark.p
% 1.61/6.28 % SZS status Theorem for theBenchmark.p
% 1.61/6.28
% 1.61/6.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.61/6.28
% 1.61/6.28 % ------ iProver source info
% 1.61/6.28
% 1.61/6.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.61/6.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.61/6.28 % git: non_committed_changes: false
% 1.61/6.28
% 1.61/6.28 % ------ Parsing...
% 1.61/6.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.61/6.28
% 1.61/6.28 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 1.61/6.28
% 1.61/6.28 % ------ Preprocessing...% ------ preprocesses with Option_epr_horn
% 1.61/6.28 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.61/6.28 % ------ Proving...
% 1.61/6.28 % ------ Problem Properties
% 1.61/6.28
% 1.61/6.28 %
% 1.61/6.28 % clauses 3
% 1.61/6.28 % conjectures 0
% 1.61/6.28 % EPR 3
% 1.61/6.28 % Horn 3
% 1.61/6.28 % unary 2
% 1.61/6.28 % binary 1
% 1.61/6.28 % lits 4
% 1.61/6.28 % lits eq 0
% 1.61/6.28 % fd_pure 0
% 1.61/6.28 % fd_pseudo 0
% 1.61/6.28 % fd_cond 0
% 1.61/6.28 % fd_pseudo_cond 0
% 1.61/6.28 % AC symbols 0
% 1.61/6.28
% 1.61/6.28 % ------ Schedule EPR Horn non eq is on
% 1.61/6.28
% 1.61/6.28 % ------ no conjectures: strip conj schedule
% 1.61/6.28
% 1.61/6.28 % ------ no equalities: superposition off
% 1.61/6.28
% 1.61/6.28 % ------ Option_epr_horn stripped conjectures Time Limit: Unbounded
% 1.61/6.28
% 1.61/6.28
% 1.61/6.28 % ------
% 1.61/6.28 % Current options:
% 1.61/6.28 % ------
% 1.61/6.28
% 1.61/6.28
% 1.61/6.28 %
% 1.61/6.28
% 1.61/6.28 % ------ Proving...
% 1.61/6.28 %
% 1.61/6.28
% 1.61/6.28 % SZS status Theorem for theBenchmark.p
% 1.61/6.28
% 1.61/6.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.61/6.28
% 1.61/6.28
%------------------------------------------------------------------------------