TSTP Solution File: MGT036+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT036+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 : 600s
% DateTime : Sun Jul 17 22:19:44 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 7
% Syntax : Number of formulae : 68 ( 18 unt; 0 def)
% Number of atoms : 198 ( 0 equ)
% Maximal formula atoms : 13 ( 2 avg)
% Number of connectives : 245 ( 115 ~; 96 |; 20 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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 : 115 ( 12 sgn 75 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_symmetry_of_FM_and_EP,axiom,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> subpopulations(efficient_producers,first_movers,E,T) ) ).
fof(mp_time_point_occur,axiom,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> in_environment(E,T) ) ).
fof(mp_growth_rate_relationships,axiom,
! [E,S1,S2,T] :
( ( ( environment(E)
& subpopulations(S1,S2,E,T) )
=> greater_or_equal(growth_rate(S1,T),zero) )
<=> ~ greater(zero,growth_rate(S1,T)) ) ).
fof(d2,hypothesis,
! [E,S1,S2,T] :
( ( environment(E)
& subpopulations(S1,S2,E,T) )
=> ( ( greater_or_equal(growth_rate(S2,T),zero)
& greater(zero,growth_rate(S1,T)) )
<=> outcompetes(S2,S1,T) ) ) ).
fof(a12,hypothesis,
! [E,S1,S2,T] :
( ( environment(E)
& in_environment(E,T)
& ~ greater(zero,growth_rate(S1,T))
& greater(resilience(S2),resilience(S1)) )
=> ~ greater(zero,growth_rate(S2,T)) ) ).
fof(a2,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)) ).
fof(prove_t5,conjecture,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> ~ outcompetes(first_movers,efficient_producers,T) ) ).
fof(subgoal_0,plain,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> ~ outcompetes(first_movers,efficient_producers,T) ),
inference(strip,[],[prove_t5]) ).
fof(negate_0_0,plain,
~ ! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> ~ outcompetes(first_movers,efficient_producers,T) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [E,T] :
( environment(E)
& outcompetes(first_movers,efficient_producers,T)
& subpopulations(first_movers,efficient_producers,E,T) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( environment(skolemFOFtoCNF_E)
& outcompetes(first_movers,efficient_producers,skolemFOFtoCNF_T)
& subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [E,T] :
( ~ environment(E)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| in_environment(E,T) ),
inference(canonicalize,[],[mp_time_point_occur]) ).
fof(normalize_0_4,plain,
! [E,T] :
( ~ environment(E)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| in_environment(E,T) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
environment(skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_6,plain,
! [E,T] :
( ~ environment(E)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| subpopulations(efficient_producers,first_movers,E,T) ),
inference(canonicalize,[],[mp_symmetry_of_FM_and_EP]) ).
fof(normalize_0_7,plain,
! [E,T] :
( ~ environment(E)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| subpopulations(efficient_producers,first_movers,E,T) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [E,S1,S2,T] :
( ~ environment(E)
| ~ subpopulations(S1,S2,E,T)
| ( ~ outcompetes(S2,S1,T)
<=> ( ~ greater(zero,growth_rate(S1,T))
| ~ greater_or_equal(growth_rate(S2,T),zero) ) ) ),
inference(canonicalize,[],[d2]) ).
fof(normalize_0_9,plain,
! [E,S1,S2,T] :
( ~ environment(E)
| ~ subpopulations(S1,S2,E,T)
| ( ~ outcompetes(S2,S1,T)
<=> ( ~ greater(zero,growth_rate(S1,T))
| ~ greater_or_equal(growth_rate(S2,T),zero) ) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [E,S1,S2,T] :
( ( ~ environment(E)
| ~ outcompetes(S2,S1,T)
| ~ subpopulations(S1,S2,E,T)
| greater(zero,growth_rate(S1,T)) )
& ( ~ environment(E)
| ~ outcompetes(S2,S1,T)
| ~ subpopulations(S1,S2,E,T)
| greater_or_equal(growth_rate(S2,T),zero) )
& ( ~ environment(E)
| ~ greater(zero,growth_rate(S1,T))
| ~ greater_or_equal(growth_rate(S2,T),zero)
| ~ subpopulations(S1,S2,E,T)
| outcompetes(S2,S1,T) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [E,S1,S2,T] :
( ~ environment(E)
| ~ outcompetes(S2,S1,T)
| ~ subpopulations(S1,S2,E,T)
| greater(zero,growth_rate(S1,T)) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
outcompetes(first_movers,efficient_producers,skolemFOFtoCNF_T),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_13,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(canonicalize,[],[a2]) ).
fof(normalize_0_14,plain,
! [E,S1,S2,T] :
( ~ environment(E)
| ~ greater(resilience(S2),resilience(S1))
| ~ greater(zero,growth_rate(S2,T))
| ~ in_environment(E,T)
| greater(zero,growth_rate(S1,T)) ),
inference(canonicalize,[],[a12]) ).
fof(normalize_0_15,plain,
! [E,S1,S2,T] :
( ~ environment(E)
| ~ greater(resilience(S2),resilience(S1))
| ~ greater(zero,growth_rate(S2,T))
| ~ in_environment(E,T)
| greater(zero,growth_rate(S1,T)) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [E,S1,S2,T] :
( ~ greater(zero,growth_rate(S1,T))
<=> ( ~ environment(E)
| ~ subpopulations(S1,S2,E,T)
| greater_or_equal(growth_rate(S1,T),zero) ) ),
inference(canonicalize,[],[mp_growth_rate_relationships]) ).
fof(normalize_0_17,plain,
! [E,S1,S2,T] :
( ~ greater(zero,growth_rate(S1,T))
<=> ( ~ environment(E)
| ~ subpopulations(S1,S2,E,T)
| greater_or_equal(growth_rate(S1,T),zero) ) ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [E,S1,S2,T] :
( ( ~ greater(zero,growth_rate(S1,T))
| ~ greater_or_equal(growth_rate(S1,T),zero) )
& ( ~ greater(zero,growth_rate(S1,T))
| environment(E) )
& ( ~ greater(zero,growth_rate(S1,T))
| subpopulations(S1,S2,E,T) )
& ( ~ environment(E)
| ~ subpopulations(S1,S2,E,T)
| greater(zero,growth_rate(S1,T))
| greater_or_equal(growth_rate(S1,T),zero) ) ),
inference(clausify,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [E,S1,T] :
( ~ greater(zero,growth_rate(S1,T))
| environment(E) ),
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [S1,T] :
( ~ greater(zero,growth_rate(S1,T))
| ~ greater_or_equal(growth_rate(S1,T),zero) ),
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_21,plain,
! [E,S1,S2,T] :
( ~ environment(E)
| ~ outcompetes(S2,S1,T)
| ~ subpopulations(S1,S2,E,T)
| greater_or_equal(growth_rate(S2,T),zero) ),
inference(conjunct,[],[normalize_0_10]) ).
cnf(refute_0_0,plain,
subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ environment(E)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| in_environment(E,T) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(subst,[],[refute_0_1:[bind(E,$fot(skolemFOFtoCNF_E)),bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_3,plain,
( ~ environment(skolemFOFtoCNF_E)
| in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
environment(skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ environment(E)
| ~ subpopulations(first_movers,efficient_producers,E,T)
| subpopulations(efficient_producers,first_movers,E,T) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_7,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| subpopulations(efficient_producers,first_movers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(subst,[],[refute_0_6:[bind(E,$fot(skolemFOFtoCNF_E)),bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_8,plain,
( ~ environment(skolemFOFtoCNF_E)
| subpopulations(efficient_producers,first_movers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_0,refute_0_7]) ).
cnf(refute_0_9,plain,
subpopulations(efficient_producers,first_movers,skolemFOFtoCNF_E,skolemFOFtoCNF_T),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ environment(E)
| ~ outcompetes(S2,S1,T)
| ~ subpopulations(S1,S2,E,T)
| greater(zero,growth_rate(S1,T)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_11,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ outcompetes(first_movers,efficient_producers,skolemFOFtoCNF_T)
| ~ subpopulations(efficient_producers,first_movers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| greater(zero,growth_rate(efficient_producers,skolemFOFtoCNF_T)) ),
inference(subst,[],[refute_0_10:[bind(E,$fot(skolemFOFtoCNF_E)),bind(S1,$fot(efficient_producers)),bind(S2,$fot(first_movers)),bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_12,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ outcompetes(first_movers,efficient_producers,skolemFOFtoCNF_T)
| greater(zero,growth_rate(efficient_producers,skolemFOFtoCNF_T)) ),
inference(resolve,[$cnf( subpopulations(efficient_producers,first_movers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ outcompetes(first_movers,efficient_producers,skolemFOFtoCNF_T)
| greater(zero,growth_rate(efficient_producers,skolemFOFtoCNF_T)) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
outcompetes(first_movers,efficient_producers,skolemFOFtoCNF_T),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_15,plain,
greater(zero,growth_rate(efficient_producers,skolemFOFtoCNF_T)),
inference(resolve,[$cnf( outcompetes(first_movers,efficient_producers,skolemFOFtoCNF_T) )],[refute_0_14,refute_0_13]) ).
cnf(refute_0_16,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_17,plain,
( ~ environment(E)
| ~ greater(resilience(S2),resilience(S1))
| ~ greater(zero,growth_rate(S2,T))
| ~ in_environment(E,T)
| greater(zero,growth_rate(S1,T)) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_18,plain,
( ~ greater(zero,growth_rate(S1,T))
| environment(E) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_19,plain,
( ~ greater(zero,growth_rate(efficient_producers,skolemFOFtoCNF_T))
| environment(E) ),
inference(subst,[],[refute_0_18:[bind(S1,$fot(efficient_producers)),bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_20,plain,
environment(E),
inference(resolve,[$cnf( greater(zero,growth_rate(efficient_producers,skolemFOFtoCNF_T)) )],[refute_0_15,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ greater(resilience(S2),resilience(S1))
| ~ greater(zero,growth_rate(S2,T))
| ~ in_environment(E,T)
| greater(zero,growth_rate(S1,T)) ),
inference(resolve,[$cnf( environment(E) )],[refute_0_20,refute_0_17]) ).
cnf(refute_0_22,plain,
( ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ greater(zero,growth_rate(efficient_producers,X_32))
| ~ in_environment(X_29,X_32)
| greater(zero,growth_rate(first_movers,X_32)) ),
inference(subst,[],[refute_0_21:[bind(E,$fot(X_29)),bind(S1,$fot(first_movers)),bind(S2,$fot(efficient_producers)),bind(T,$fot(X_32))]]) ).
cnf(refute_0_23,plain,
( ~ greater(zero,growth_rate(efficient_producers,X_32))
| ~ in_environment(X_29,X_32)
| greater(zero,growth_rate(first_movers,X_32)) ),
inference(resolve,[$cnf( greater(resilience(efficient_producers),resilience(first_movers)) )],[refute_0_16,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ greater(zero,growth_rate(efficient_producers,skolemFOFtoCNF_T))
| ~ in_environment(X_33,skolemFOFtoCNF_T)
| greater(zero,growth_rate(first_movers,skolemFOFtoCNF_T)) ),
inference(subst,[],[refute_0_23:[bind(X_29,$fot(X_33)),bind(X_32,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_25,plain,
( ~ in_environment(X_33,skolemFOFtoCNF_T)
| greater(zero,growth_rate(first_movers,skolemFOFtoCNF_T)) ),
inference(resolve,[$cnf( greater(zero,growth_rate(efficient_producers,skolemFOFtoCNF_T)) )],[refute_0_15,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ greater(zero,growth_rate(S1,T))
| ~ greater_or_equal(growth_rate(S1,T),zero) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_27,plain,
( ~ greater(zero,growth_rate(first_movers,skolemFOFtoCNF_T))
| ~ greater_or_equal(growth_rate(first_movers,skolemFOFtoCNF_T),zero) ),
inference(subst,[],[refute_0_26:[bind(S1,$fot(first_movers)),bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_28,plain,
( ~ environment(E)
| ~ outcompetes(S2,S1,T)
| ~ subpopulations(S1,S2,E,T)
| greater_or_equal(growth_rate(S2,T),zero) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_29,plain,
( ~ outcompetes(S2,S1,T)
| ~ subpopulations(S1,S2,E,T)
| greater_or_equal(growth_rate(S2,T),zero) ),
inference(resolve,[$cnf( environment(E) )],[refute_0_20,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ outcompetes(first_movers,efficient_producers,skolemFOFtoCNF_T)
| ~ subpopulations(efficient_producers,first_movers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| greater_or_equal(growth_rate(first_movers,skolemFOFtoCNF_T),zero) ),
inference(subst,[],[refute_0_29:[bind(E,$fot(skolemFOFtoCNF_E)),bind(S1,$fot(efficient_producers)),bind(S2,$fot(first_movers)),bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_31,plain,
( ~ outcompetes(first_movers,efficient_producers,skolemFOFtoCNF_T)
| greater_or_equal(growth_rate(first_movers,skolemFOFtoCNF_T),zero) ),
inference(resolve,[$cnf( subpopulations(efficient_producers,first_movers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_9,refute_0_30]) ).
cnf(refute_0_32,plain,
greater_or_equal(growth_rate(first_movers,skolemFOFtoCNF_T),zero),
inference(resolve,[$cnf( outcompetes(first_movers,efficient_producers,skolemFOFtoCNF_T) )],[refute_0_14,refute_0_31]) ).
cnf(refute_0_33,plain,
~ greater(zero,growth_rate(first_movers,skolemFOFtoCNF_T)),
inference(resolve,[$cnf( greater_or_equal(growth_rate(first_movers,skolemFOFtoCNF_T),zero) )],[refute_0_32,refute_0_27]) ).
cnf(refute_0_34,plain,
~ in_environment(X_33,skolemFOFtoCNF_T),
inference(resolve,[$cnf( greater(zero,growth_rate(first_movers,skolemFOFtoCNF_T)) )],[refute_0_25,refute_0_33]) ).
cnf(refute_0_35,plain,
~ in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T),
inference(subst,[],[refute_0_34:[bind(X_33,$fot(skolemFOFtoCNF_E))]]) ).
cnf(refute_0_36,plain,
$false,
inference(resolve,[$cnf( in_environment(skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_5,refute_0_35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : MGT036+1 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.12/0.35 % Computer : n025.cluster.edu
% 0.12/0.35 % Model : x86_64 x86_64
% 0.12/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35 % Memory : 8042.1875MB
% 0.12/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35 % CPULimit : 300
% 0.12/0.35 % WCLimit : 600
% 0.12/0.35 % DateTime : Thu Jun 9 09:54:05 EDT 2022
% 0.12/0.35 % CPUTime :
% 0.12/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.38
%------------------------------------------------------------------------------