TSTP Solution File: MGT036+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : MGT036+1 : TPTP v8.1.2. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n005.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 09:14:27 EDT 2023
% Result : Theorem 1.67s 1.13s
% Output : CNFRefutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 8
% Syntax : Number of formulae : 68 ( 10 unt; 0 def)
% Number of atoms : 232 ( 0 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 286 ( 122 ~; 107 |; 38 &)
% ( 8 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 158 ( 11 sgn; 105 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> subpopulations(efficient_producers,first_movers,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_symmetry_of_FM_and_EP) ).
fof(f2,axiom,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> in_environment(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur) ).
fof(f3,axiom,
! [X0,X2,X3,X1] :
( ( ( subpopulations(X2,X3,X0,X1)
& environment(X0) )
=> greater_or_equal(growth_rate(X2,X1),zero) )
<=> ~ greater(zero,growth_rate(X2,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_relationships) ).
fof(f4,axiom,
! [X0,X2,X3,X1] :
( ( subpopulations(X2,X3,X0,X1)
& environment(X0) )
=> ( ( greater(zero,growth_rate(X2,X1))
& greater_or_equal(growth_rate(X3,X1),zero) )
<=> outcompetes(X3,X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
fof(f5,axiom,
! [X0,X2,X3,X1] :
( ( greater(resilience(X3),resilience(X2))
& ~ greater(zero,growth_rate(X2,X1))
& in_environment(X0,X1)
& environment(X0) )
=> ~ greater(zero,growth_rate(X3,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a12) ).
fof(f6,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
fof(f7,conjecture,
! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ~ outcompetes(first_movers,efficient_producers,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( ( subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ~ outcompetes(first_movers,efficient_producers,X1) ),
inference(negated_conjecture,[],[f7]) ).
fof(f9,plain,
! [X0,X1,X2,X3] :
( ( ( subpopulations(X1,X2,X0,X3)
& environment(X0) )
=> greater_or_equal(growth_rate(X1,X3),zero) )
<=> ~ greater(zero,growth_rate(X1,X3)) ),
inference(rectify,[],[f3]) ).
fof(f10,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(rectify,[],[f4]) ).
fof(f11,plain,
! [X0,X1,X2,X3] :
( ( greater(resilience(X2),resilience(X1))
& ~ greater(zero,growth_rate(X1,X3))
& in_environment(X0,X3)
& environment(X0) )
=> ~ greater(zero,growth_rate(X2,X3)) ),
inference(rectify,[],[f5]) ).
fof(f12,plain,
! [X0,X1] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f13,plain,
! [X0,X1] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f15,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(flattening,[],[f14]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( ( greater_or_equal(growth_rate(X1,X3),zero)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) )
<=> ~ greater(zero,growth_rate(X1,X3)) ),
inference(ennf_transformation,[],[f9]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( ( greater_or_equal(growth_rate(X1,X3),zero)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) )
<=> ~ greater(zero,growth_rate(X1,X3)) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1,X2,X3] :
( ( ( greater(zero,growth_rate(X1,X3))
& greater_or_equal(growth_rate(X2,X3),zero) )
<=> outcompetes(X2,X1,X3) )
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f19,plain,
! [X0,X1,X2,X3] :
( ( ( greater(zero,growth_rate(X1,X3))
& greater_or_equal(growth_rate(X2,X3),zero) )
<=> outcompetes(X2,X1,X3) )
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(flattening,[],[f18]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( ~ greater(zero,growth_rate(X2,X3))
| ~ greater(resilience(X2),resilience(X1))
| greater(zero,growth_rate(X1,X3))
| ~ in_environment(X0,X3)
| ~ environment(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( ~ greater(zero,growth_rate(X2,X3))
| ~ greater(resilience(X2),resilience(X1))
| greater(zero,growth_rate(X1,X3))
| ~ in_environment(X0,X3)
| ~ environment(X0) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
? [X0,X1] :
( outcompetes(first_movers,efficient_producers,X1)
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f23,plain,
? [X0,X1] :
( outcompetes(first_movers,efficient_producers,X1)
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( ( greater_or_equal(growth_rate(X1,X3),zero)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| greater(zero,growth_rate(X1,X3)) )
& ( ~ greater(zero,growth_rate(X1,X3))
| ( ~ greater_or_equal(growth_rate(X1,X3),zero)
& subpopulations(X1,X2,X0,X3)
& environment(X0) ) ) ),
inference(nnf_transformation,[],[f17]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( ( greater_or_equal(growth_rate(X1,X3),zero)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| greater(zero,growth_rate(X1,X3)) )
& ( ~ greater(zero,growth_rate(X1,X3))
| ( ~ greater_or_equal(growth_rate(X1,X3),zero)
& subpopulations(X1,X2,X0,X3)
& environment(X0) ) ) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( ( ( ( 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) ) )
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(nnf_transformation,[],[f19]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( ( ( ( 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) ) )
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
( ? [X0,X1] :
( outcompetes(first_movers,efficient_producers,X1)
& subpopulations(first_movers,efficient_producers,X0,X1)
& environment(X0) )
=> ( outcompetes(first_movers,efficient_producers,sK1)
& subpopulations(first_movers,efficient_producers,sK0,sK1)
& environment(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f29,plain,
( outcompetes(first_movers,efficient_producers,sK1)
& subpopulations(first_movers,efficient_producers,sK0,sK1)
& environment(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f23,f28]) ).
fof(f30,plain,
! [X0,X1] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f13]) ).
fof(f31,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f15]) ).
fof(f32,plain,
! [X3,X0,X1] :
( ~ greater(zero,growth_rate(X1,X3))
| environment(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( ~ greater(zero,growth_rate(X1,X3))
| subpopulations(X1,X2,X0,X3) ),
inference(cnf_transformation,[],[f25]) ).
fof(f34,plain,
! [X3,X1] :
( ~ greater(zero,growth_rate(X1,X3))
| ~ greater_or_equal(growth_rate(X1,X3),zero) ),
inference(cnf_transformation,[],[f25]) ).
fof(f37,plain,
! [X2,X3,X0,X1] :
( greater_or_equal(growth_rate(X2,X3),zero)
| ~ outcompetes(X2,X1,X3)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f38,plain,
! [X2,X3,X0,X1] :
( greater(zero,growth_rate(X1,X3))
| ~ outcompetes(X2,X1,X3)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f39,plain,
! [X2,X3,X0,X1] :
( ~ greater(zero,growth_rate(X2,X3))
| ~ greater(resilience(X2),resilience(X1))
| greater(zero,growth_rate(X1,X3))
| ~ in_environment(X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[],[f21]) ).
fof(f40,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf_transformation,[],[f6]) ).
fof(f41,plain,
environment(sK0),
inference(cnf_transformation,[],[f29]) ).
fof(f42,plain,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f29]) ).
fof(f43,plain,
outcompetes(first_movers,efficient_producers,sK1),
inference(cnf_transformation,[],[f29]) ).
cnf(c_49,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| subpopulations(efficient_producers,first_movers,X0,X1) ),
inference(cnf_transformation,[],[f30]) ).
cnf(c_50,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
cnf(c_52,plain,
( ~ greater_or_equal(growth_rate(X0,X1),zero)
| ~ greater(zero,growth_rate(X0,X1)) ),
inference(cnf_transformation,[],[f34]) ).
cnf(c_53,plain,
( ~ greater(zero,growth_rate(X0,X1))
| subpopulations(X0,X2,X3,X1) ),
inference(cnf_transformation,[],[f33]) ).
cnf(c_54,plain,
( ~ greater(zero,growth_rate(X0,X1))
| environment(X2) ),
inference(cnf_transformation,[],[f32]) ).
cnf(c_55,plain,
( ~ subpopulations(X0,X1,X2,X3)
| ~ outcompetes(X1,X0,X3)
| ~ environment(X2)
| greater(zero,growth_rate(X0,X3)) ),
inference(cnf_transformation,[],[f38]) ).
cnf(c_56,plain,
( ~ subpopulations(X0,X1,X2,X3)
| ~ outcompetes(X1,X0,X3)
| ~ environment(X2)
| greater_or_equal(growth_rate(X1,X3),zero) ),
inference(cnf_transformation,[],[f37]) ).
cnf(c_58,plain,
( ~ greater(resilience(X0),resilience(X1))
| ~ greater(zero,growth_rate(X0,X2))
| ~ in_environment(X3,X2)
| ~ environment(X3)
| greater(zero,growth_rate(X1,X2)) ),
inference(cnf_transformation,[],[f39]) ).
cnf(c_59,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf_transformation,[],[f40]) ).
cnf(c_60,negated_conjecture,
outcompetes(first_movers,efficient_producers,sK1),
inference(cnf_transformation,[],[f43]) ).
cnf(c_61,negated_conjecture,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f42]) ).
cnf(c_62,negated_conjecture,
environment(sK0),
inference(cnf_transformation,[],[f41]) ).
cnf(c_84,plain,
( ~ greater(resilience(X0),resilience(X1))
| ~ greater(zero,growth_rate(X0,X2))
| ~ in_environment(X3,X2)
| greater(zero,growth_rate(X1,X2)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_58,c_54]) ).
cnf(c_146,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater(resilience(X2),resilience(X3))
| ~ greater(zero,growth_rate(X2,X1))
| ~ environment(X0)
| greater(zero,growth_rate(X3,X1)) ),
inference(resolution,[status(thm)],[c_50,c_84]) ).
cnf(c_157,plain,
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ greater(resilience(X2),resilience(X3))
| ~ greater(zero,growth_rate(X2,X1))
| greater(zero,growth_rate(X3,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_146,c_54]) ).
cnf(c_166,plain,
( ~ subpopulations(efficient_producers,first_movers,X0,sK1)
| ~ environment(X0)
| greater_or_equal(growth_rate(first_movers,sK1),zero) ),
inference(resolution,[status(thm)],[c_56,c_60]) ).
cnf(c_177,plain,
( ~ subpopulations(efficient_producers,first_movers,X0,sK1)
| ~ environment(X0)
| greater(zero,growth_rate(efficient_producers,sK1)) ),
inference(resolution,[status(thm)],[c_55,c_60]) ).
cnf(c_197,plain,
( ~ subpopulations(efficient_producers,first_movers,X0,sK1)
| ~ greater(zero,growth_rate(first_movers,sK1))
| ~ environment(X0) ),
inference(resolution,[status(thm)],[c_52,c_166]) ).
cnf(c_205,plain,
( ~ subpopulations(efficient_producers,first_movers,X0,sK1)
| ~ greater(zero,growth_rate(first_movers,sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_197,c_54]) ).
cnf(c_233,plain,
( ~ subpopulations(efficient_producers,first_movers,sK0,sK1)
| greater(zero,growth_rate(efficient_producers,sK1)) ),
inference(resolution,[status(thm)],[c_177,c_62]) ).
cnf(c_345,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,sK1)
| ~ environment(sK0)
| subpopulations(efficient_producers,first_movers,sK0,sK1) ),
inference(instantiation,[status(thm)],[c_49]) ).
cnf(c_346,plain,
( ~ greater(resilience(X0),resilience(X1))
| ~ greater(zero,growth_rate(X0,sK1))
| ~ subpopulations(first_movers,efficient_producers,sK0,sK1)
| greater(zero,growth_rate(X1,sK1)) ),
inference(instantiation,[status(thm)],[c_157]) ).
cnf(c_348,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK1))
| subpopulations(efficient_producers,X0,X1,sK1) ),
inference(instantiation,[status(thm)],[c_53]) ).
cnf(c_350,plain,
( ~ greater(resilience(efficient_producers),resilience(X0))
| ~ subpopulations(first_movers,efficient_producers,sK0,sK1)
| ~ greater(zero,growth_rate(efficient_producers,sK1))
| greater(zero,growth_rate(X0,sK1)) ),
inference(instantiation,[status(thm)],[c_346]) ).
cnf(c_352,plain,
( ~ subpopulations(first_movers,efficient_producers,sK0,sK1)
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ greater(zero,growth_rate(efficient_producers,sK1))
| greater(zero,growth_rate(first_movers,sK1)) ),
inference(instantiation,[status(thm)],[c_350]) ).
cnf(c_353,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK1))
| subpopulations(efficient_producers,first_movers,X0,sK1) ),
inference(instantiation,[status(thm)],[c_348]) ).
cnf(c_354,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_353,c_352,c_345,c_233,c_205,c_59,c_61,c_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT036+1 : TPTP v8.1.2. Released v2.0.0.
% 0.11/0.12 % Command : run_iprover %s %d THM
% 0.13/0.33 % Computer : n005.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 28 06:19:23 EDT 2023
% 0.20/0.33 % CPUTime :
% 0.20/0.46 Running first-order theorem proving
% 0.20/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 1.67/1.13 % SZS status Started for theBenchmark.p
% 1.67/1.13 % SZS status Theorem for theBenchmark.p
% 1.67/1.13
% 1.67/1.13 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.67/1.13
% 1.67/1.13 ------ iProver source info
% 1.67/1.13
% 1.67/1.13 git: date: 2023-05-31 18:12:56 +0000
% 1.67/1.13 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.67/1.13 git: non_committed_changes: false
% 1.67/1.13 git: last_make_outside_of_git: false
% 1.67/1.13
% 1.67/1.13 ------ Parsing...
% 1.67/1.13 ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.67/1.13
% 1.67/1.13 ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e
% 1.67/1.13
% 1.67/1.13 ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.67/1.13 ------ Proving...
% 1.67/1.13 ------ Problem Properties
% 1.67/1.13
% 1.67/1.13
% 1.67/1.13 clauses 11
% 1.67/1.13 conjectures 2
% 1.67/1.13 EPR 5
% 1.67/1.13 Horn 10
% 1.67/1.13 unary 3
% 1.67/1.13 binary 5
% 1.67/1.13 lits 23
% 1.67/1.13 lits eq 0
% 1.67/1.13 fd_pure 0
% 1.67/1.13 fd_pseudo 0
% 1.67/1.13 fd_cond 0
% 1.67/1.13 fd_pseudo_cond 0
% 1.67/1.13 AC symbols 0
% 1.67/1.13
% 1.67/1.13 ------ Schedule dynamic 5 is on
% 1.67/1.13
% 1.67/1.13 ------ no equalities: superposition off
% 1.67/1.13
% 1.67/1.13 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.67/1.13
% 1.67/1.13
% 1.67/1.13 ------
% 1.67/1.13 Current options:
% 1.67/1.13 ------
% 1.67/1.13
% 1.67/1.13
% 1.67/1.13
% 1.67/1.13
% 1.67/1.13 ------ Proving...
% 1.67/1.13
% 1.67/1.13
% 1.67/1.13 % SZS status Theorem for theBenchmark.p
% 1.67/1.13
% 1.67/1.13 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.67/1.14
% 1.67/1.14
%------------------------------------------------------------------------------