TSTP Solution File: MGT032+2 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : MGT032+2 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 09:14:20 EDT 2023
% Result : Theorem 0.80s 1.17s
% Output : CNFRefutation 0.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 5 unt; 0 def)
% Number of atoms : 164 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 204 ( 79 ~; 65 |; 46 &)
% ( 0 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% 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 : 77 ( 0 sgn; 47 !; 16 ?)
% 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) )
=> ? [X4] :
( ! [X3] :
( ( greater_or_equal(X3,X4)
& subpopulations(first_movers,efficient_producers,X0,X3) )
=> greater(growth_rate(efficient_producers,X3),growth_rate(first_movers,X3)) )
& in_environment(X0,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1) ).
fof(f3,conjecture,
! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X4] :
( ! [X3] :
( ( greater_or_equal(X3,X4)
& subpopulations(first_movers,efficient_producers,X0,X3) )
=> selection_favors(efficient_producers,first_movers,X3) )
& in_environment(X0,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t1) ).
fof(f4,negated_conjecture,
~ ! [X0] :
( ( stable(X0)
& environment(X0) )
=> ? [X4] :
( ! [X3] :
( ( greater_or_equal(X3,X4)
& subpopulations(first_movers,efficient_producers,X0,X3) )
=> selection_favors(efficient_producers,first_movers,X3) )
& in_environment(X0,X4) ) ),
inference(negated_conjecture,[],[f3]) ).
fof(f5,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(rectify,[],[f2]) ).
fof(f6,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(rectify,[],[f4]) ).
fof(f7,plain,
! [X0,X1,X2,X3] :
( selection_favors(X2,X1,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f8,plain,
! [X0,X1,X2,X3] :
( selection_favors(X2,X1,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(flattening,[],[f7]) ).
fof(f9,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& in_environment(X0,X1) )
| ~ stable(X0)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f10,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& in_environment(X0,X1) )
| ~ stable(X0)
| ~ environment(X0) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
? [X0] :
( ! [X1] :
( ? [X2] :
( ~ selection_favors(efficient_producers,first_movers,X2)
& greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
| ~ in_environment(X0,X1) )
& stable(X0)
& environment(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f12,plain,
? [X0] :
( ! [X1] :
( ? [X2] :
( ~ selection_favors(efficient_producers,first_movers,X2)
& greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
| ~ in_environment(X0,X1) )
& stable(X0)
& environment(X0) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
! [X0] :
( ? [X1] :
( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& in_environment(X0,X1) )
=> ( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& in_environment(X0,sK0(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f14,plain,
! [X0] :
( ( ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2) )
& in_environment(X0,sK0(X0)) )
| ~ stable(X0)
| ~ environment(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f10,f13]) ).
fof(f15,plain,
( ? [X0] :
( ! [X1] :
( ? [X2] :
( ~ selection_favors(efficient_producers,first_movers,X2)
& greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,X0,X2) )
| ~ in_environment(X0,X1) )
& stable(X0)
& environment(X0) )
=> ( ! [X1] :
( ? [X2] :
( ~ selection_favors(efficient_producers,first_movers,X2)
& greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,sK1,X2) )
| ~ in_environment(sK1,X1) )
& stable(sK1)
& environment(sK1) ) ),
introduced(choice_axiom,[]) ).
fof(f16,plain,
! [X1] :
( ? [X2] :
( ~ selection_favors(efficient_producers,first_movers,X2)
& greater_or_equal(X2,X1)
& subpopulations(first_movers,efficient_producers,sK1,X2) )
=> ( ~ selection_favors(efficient_producers,first_movers,sK2(X1))
& greater_or_equal(sK2(X1),X1)
& subpopulations(first_movers,efficient_producers,sK1,sK2(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f17,plain,
( ! [X1] :
( ( ~ selection_favors(efficient_producers,first_movers,sK2(X1))
& greater_or_equal(sK2(X1),X1)
& subpopulations(first_movers,efficient_producers,sK1,sK2(X1)) )
| ~ in_environment(sK1,X1) )
& stable(sK1)
& environment(sK1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f12,f16,f15]) ).
fof(f18,plain,
! [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) ),
inference(cnf_transformation,[],[f8]) ).
fof(f19,plain,
! [X0] :
( in_environment(X0,sK0(X0))
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f20,plain,
! [X2,X0] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater_or_equal(X2,sK0(X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ stable(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f21,plain,
environment(sK1),
inference(cnf_transformation,[],[f17]) ).
fof(f22,plain,
stable(sK1),
inference(cnf_transformation,[],[f17]) ).
fof(f23,plain,
! [X1] :
( subpopulations(first_movers,efficient_producers,sK1,sK2(X1))
| ~ in_environment(sK1,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f24,plain,
! [X1] :
( greater_or_equal(sK2(X1),X1)
| ~ in_environment(sK1,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f25,plain,
! [X1] :
( ~ selection_favors(efficient_producers,first_movers,sK2(X1))
| ~ in_environment(sK1,X1) ),
inference(cnf_transformation,[],[f17]) ).
cnf(c_49,plain,
( ~ greater(growth_rate(X0,X1),growth_rate(X2,X1))
| ~ subpopulations(X2,X0,X3,X1)
| ~ environment(X3)
| selection_favors(X0,X2,X1) ),
inference(cnf_transformation,[],[f18]) ).
cnf(c_50,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater_or_equal(X1,sK0(X0))
| ~ environment(X0)
| ~ stable(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(cnf_transformation,[],[f20]) ).
cnf(c_51,plain,
( ~ environment(X0)
| ~ stable(X0)
| in_environment(X0,sK0(X0)) ),
inference(cnf_transformation,[],[f19]) ).
cnf(c_52,negated_conjecture,
( ~ selection_favors(efficient_producers,first_movers,sK2(X0))
| ~ in_environment(sK1,X0) ),
inference(cnf_transformation,[],[f25]) ).
cnf(c_53,negated_conjecture,
( ~ in_environment(sK1,X0)
| greater_or_equal(sK2(X0),X0) ),
inference(cnf_transformation,[],[f24]) ).
cnf(c_54,negated_conjecture,
( ~ in_environment(sK1,X0)
| subpopulations(first_movers,efficient_producers,sK1,sK2(X0)) ),
inference(cnf_transformation,[],[f23]) ).
cnf(c_55,negated_conjecture,
stable(sK1),
inference(cnf_transformation,[],[f22]) ).
cnf(c_56,negated_conjecture,
environment(sK1),
inference(cnf_transformation,[],[f21]) ).
cnf(c_60,plain,
( ~ environment(sK1)
| ~ stable(sK1)
| in_environment(sK1,sK0(sK1)) ),
inference(instantiation,[status(thm)],[c_51]) ).
cnf(c_103,plain,
( ~ greater(growth_rate(efficient_producers,sK2(X0)),growth_rate(first_movers,sK2(X0)))
| ~ subpopulations(first_movers,efficient_producers,X1,sK2(X0))
| ~ in_environment(sK1,X0)
| ~ environment(X1) ),
inference(resolution,[status(thm)],[c_49,c_52]) ).
cnf(c_121,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,sK2(sK0(X0)))
| ~ in_environment(sK1,sK0(X0))
| ~ environment(X0)
| ~ stable(X0)
| greater(growth_rate(efficient_producers,sK2(sK0(X0))),growth_rate(first_movers,sK2(sK0(X0)))) ),
inference(resolution,[status(thm)],[c_50,c_53]) ).
cnf(c_133,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,sK2(sK0(X0)))
| ~ in_environment(sK1,sK0(X0))
| ~ environment(X0)
| ~ stable(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_121,c_103]) ).
cnf(c_143,plain,
( ~ in_environment(sK1,sK0(sK1))
| ~ environment(sK1)
| ~ stable(sK1) ),
inference(resolution,[status(thm)],[c_54,c_133]) ).
cnf(c_144,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_143,c_60,c_55,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : MGT032+2 : TPTP v8.1.2. Released v2.0.0.
% 0.00/0.14 % Command : run_iprover %s %d THM
% 0.17/0.35 % Computer : n012.cluster.edu
% 0.17/0.35 % Model : x86_64 x86_64
% 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.35 % Memory : 8042.1875MB
% 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.35 % CPULimit : 300
% 0.17/0.35 % WCLimit : 300
% 0.17/0.35 % DateTime : Mon Aug 28 06:30:24 EDT 2023
% 0.17/0.35 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.80/1.17 % SZS status Started for theBenchmark.p
% 0.80/1.17 % SZS status Theorem for theBenchmark.p
% 0.80/1.17
% 0.80/1.17 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.80/1.17
% 0.80/1.17 ------ iProver source info
% 0.80/1.17
% 0.80/1.17 git: date: 2023-05-31 18:12:56 +0000
% 0.80/1.17 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.80/1.17 git: non_committed_changes: false
% 0.80/1.17 git: last_make_outside_of_git: false
% 0.80/1.17
% 0.80/1.17 ------ Parsing...
% 0.80/1.17 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.80/1.17
% 0.80/1.17 ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s
% 0.80/1.17
% 0.80/1.17 % SZS status Theorem for theBenchmark.p
% 0.80/1.17
% 0.80/1.17 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.80/1.17
% 0.80/1.18
%------------------------------------------------------------------------------