TSTP Solution File: MGT022+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT022+2 : TPTP v8.1.0. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 22:18:54 EDT 2022
% Result : Theorem 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 59 ( 26 unt; 0 def)
% Number of atoms : 185 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 219 ( 93 ~; 78 |; 35 &)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 49 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mp_constant_not_decrease,axiom,
! [X] :
( constant(X)
=> ~ decreases(X) ) ).
fof(a6,hypothesis,
! [E,S1,S2,T] :
( ( environment(E)
& subpopulations(S1,S2,E,T)
& greater(resilience(S2),resilience(S1)) )
=> ( ( decreases(resources(E,T))
=> increases(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) )
& ( constant(resources(E,T))
=> constant(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) ) ) ) ).
fof(a2,hypothesis,
greater(resilience(efficient_producers),resilience(first_movers)) ).
fof(prove_l4,conjecture,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> ( ( decreases(resources(E,T))
=> increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) )
& ( constant(resources(E,T))
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) ) ) ).
fof(subgoal_0,plain,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T)
& decreases(resources(E,T)) )
=> increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ),
inference(strip,[],[prove_l4]) ).
fof(subgoal_1,plain,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T)
& ( decreases(resources(E,T))
=> increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) )
& constant(resources(E,T)) )
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ),
inference(strip,[],[prove_l4]) ).
fof(negate_0_0,plain,
~ ! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T)
& decreases(resources(E,T)) )
=> increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [E,T] :
( ~ increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
& decreases(resources(E,T))
& environment(E)
& subpopulations(first_movers,efficient_producers,E,T) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ increases(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,skolemFOFtoCNF_T)))
& decreases(resources(skolemFOFtoCNF_E,skolemFOFtoCNF_T))
& environment(skolemFOFtoCNF_E)
& 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,S1,S2,T] :
( ~ environment(E)
| ~ greater(resilience(S2),resilience(S1))
| ~ subpopulations(S1,S2,E,T)
| ( ( ~ constant(resources(E,T))
| constant(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) )
& ( ~ decreases(resources(E,T))
| increases(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) ) ) ),
inference(canonicalize,[],[a6]) ).
fof(normalize_0_4,plain,
! [E,S1,S2,T] :
( ~ environment(E)
| ~ greater(resilience(S2),resilience(S1))
| ~ subpopulations(S1,S2,E,T)
| ( ( ~ constant(resources(E,T))
| constant(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) )
& ( ~ decreases(resources(E,T))
| increases(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) ) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [E,S1,S2,T] :
( ( ~ constant(resources(E,T))
| ~ environment(E)
| ~ greater(resilience(S2),resilience(S1))
| ~ subpopulations(S1,S2,E,T)
| constant(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) )
& ( ~ decreases(resources(E,T))
| ~ environment(E)
| ~ greater(resilience(S2),resilience(S1))
| ~ subpopulations(S1,S2,E,T)
| increases(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [E,S1,S2,T] :
( ~ decreases(resources(E,T))
| ~ environment(E)
| ~ greater(resilience(S2),resilience(S1))
| ~ subpopulations(S1,S2,E,T)
| increases(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
decreases(resources(skolemFOFtoCNF_E,skolemFOFtoCNF_T)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_8,plain,
environment(skolemFOFtoCNF_E),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_9,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(canonicalize,[],[a2]) ).
fof(normalize_0_10,plain,
~ increases(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,skolemFOFtoCNF_T))),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ decreases(resources(E,T))
| ~ environment(E)
| ~ greater(resilience(S2),resilience(S1))
| ~ subpopulations(S1,S2,E,T)
| increases(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ decreases(resources(skolemFOFtoCNF_E,skolemFOFtoCNF_T))
| ~ environment(skolemFOFtoCNF_E)
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T)
| increases(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,skolemFOFtoCNF_T))) ),
inference(subst,[],[refute_0_1:[bind(E,$fot(skolemFOFtoCNF_E)),bind(S1,$fot(first_movers)),bind(S2,$fot(efficient_producers)),bind(T,$fot(skolemFOFtoCNF_T))]]) ).
cnf(refute_0_3,plain,
( ~ decreases(resources(skolemFOFtoCNF_E,skolemFOFtoCNF_T))
| ~ environment(skolemFOFtoCNF_E)
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| increases(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,skolemFOFtoCNF_T))) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E,skolemFOFtoCNF_T) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
decreases(resources(skolemFOFtoCNF_E,skolemFOFtoCNF_T)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ environment(skolemFOFtoCNF_E)
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| increases(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,skolemFOFtoCNF_T))) ),
inference(resolve,[$cnf( decreases(resources(skolemFOFtoCNF_E,skolemFOFtoCNF_T)) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
environment(skolemFOFtoCNF_E),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_7,plain,
( ~ greater(resilience(efficient_producers),resilience(first_movers))
| increases(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,skolemFOFtoCNF_T))) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E) )],[refute_0_6,refute_0_5]) ).
cnf(refute_0_8,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_9,plain,
increases(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,skolemFOFtoCNF_T))),
inference(resolve,[$cnf( greater(resilience(efficient_producers),resilience(first_movers)) )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
~ increases(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,skolemFOFtoCNF_T))),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_11,plain,
$false,
inference(resolve,[$cnf( increases(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T),disbanding_rate(efficient_producers,skolemFOFtoCNF_T))) )],[refute_0_9,refute_0_10]) ).
fof(negate_1_0,plain,
~ ! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T)
& ( decreases(resources(E,T))
=> increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) )
& constant(resources(E,T)) )
=> ~ decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [E,T] :
( constant(resources(E,T))
& decreases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T)))
& environment(E)
& subpopulations(first_movers,efficient_producers,E,T)
& ( ~ decreases(resources(E,T))
| increases(difference(disbanding_rate(first_movers,T),disbanding_rate(efficient_producers,T))) ) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( constant(resources(skolemFOFtoCNF_E_1,skolemFOFtoCNF_T_1))
& decreases(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T_1),disbanding_rate(efficient_producers,skolemFOFtoCNF_T_1)))
& environment(skolemFOFtoCNF_E_1)
& subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E_1,skolemFOFtoCNF_T_1)
& ( ~ decreases(resources(skolemFOFtoCNF_E_1,skolemFOFtoCNF_T_1))
| increases(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T_1),disbanding_rate(efficient_producers,skolemFOFtoCNF_T_1))) ) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E_1,skolemFOFtoCNF_T_1),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
! [E,S1,S2,T] :
( ~ environment(E)
| ~ greater(resilience(S2),resilience(S1))
| ~ subpopulations(S1,S2,E,T)
| ( ( ~ constant(resources(E,T))
| constant(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) )
& ( ~ decreases(resources(E,T))
| increases(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) ) ) ),
inference(canonicalize,[],[a6]) ).
fof(normalize_1_4,plain,
! [E,S1,S2,T] :
( ~ environment(E)
| ~ greater(resilience(S2),resilience(S1))
| ~ subpopulations(S1,S2,E,T)
| ( ( ~ constant(resources(E,T))
| constant(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) )
& ( ~ decreases(resources(E,T))
| increases(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) ) ) ),
inference(specialize,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [E,S1,S2,T] :
( ( ~ constant(resources(E,T))
| ~ environment(E)
| ~ greater(resilience(S2),resilience(S1))
| ~ subpopulations(S1,S2,E,T)
| constant(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) )
& ( ~ decreases(resources(E,T))
| ~ environment(E)
| ~ greater(resilience(S2),resilience(S1))
| ~ subpopulations(S1,S2,E,T)
| increases(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) ) ),
inference(clausify,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [E,S1,S2,T] :
( ~ constant(resources(E,T))
| ~ environment(E)
| ~ greater(resilience(S2),resilience(S1))
| ~ subpopulations(S1,S2,E,T)
| constant(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) ),
inference(conjunct,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
constant(resources(skolemFOFtoCNF_E_1,skolemFOFtoCNF_T_1)),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_8,plain,
environment(skolemFOFtoCNF_E_1),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_9,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(canonicalize,[],[a2]) ).
fof(normalize_1_10,plain,
decreases(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T_1),disbanding_rate(efficient_producers,skolemFOFtoCNF_T_1))),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_11,plain,
! [X] :
( ~ constant(X)
| ~ decreases(X) ),
inference(canonicalize,[],[mp_constant_not_decrease]) ).
fof(normalize_1_12,plain,
! [X] :
( ~ constant(X)
| ~ decreases(X) ),
inference(specialize,[],[normalize_1_11]) ).
cnf(refute_1_0,plain,
subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E_1,skolemFOFtoCNF_T_1),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
( ~ constant(resources(E,T))
| ~ environment(E)
| ~ greater(resilience(S2),resilience(S1))
| ~ subpopulations(S1,S2,E,T)
| constant(difference(disbanding_rate(S1,T),disbanding_rate(S2,T))) ),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_2,plain,
( ~ constant(resources(skolemFOFtoCNF_E_1,skolemFOFtoCNF_T_1))
| ~ environment(skolemFOFtoCNF_E_1)
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E_1,skolemFOFtoCNF_T_1)
| constant(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T_1),disbanding_rate(efficient_producers,skolemFOFtoCNF_T_1))) ),
inference(subst,[],[refute_1_1:[bind(E,$fot(skolemFOFtoCNF_E_1)),bind(S1,$fot(first_movers)),bind(S2,$fot(efficient_producers)),bind(T,$fot(skolemFOFtoCNF_T_1))]]) ).
cnf(refute_1_3,plain,
( ~ constant(resources(skolemFOFtoCNF_E_1,skolemFOFtoCNF_T_1))
| ~ environment(skolemFOFtoCNF_E_1)
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| constant(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T_1),disbanding_rate(efficient_producers,skolemFOFtoCNF_T_1))) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,skolemFOFtoCNF_E_1,skolemFOFtoCNF_T_1) )],[refute_1_0,refute_1_2]) ).
cnf(refute_1_4,plain,
constant(resources(skolemFOFtoCNF_E_1,skolemFOFtoCNF_T_1)),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_5,plain,
( ~ environment(skolemFOFtoCNF_E_1)
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| constant(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T_1),disbanding_rate(efficient_producers,skolemFOFtoCNF_T_1))) ),
inference(resolve,[$cnf( constant(resources(skolemFOFtoCNF_E_1,skolemFOFtoCNF_T_1)) )],[refute_1_4,refute_1_3]) ).
cnf(refute_1_6,plain,
environment(skolemFOFtoCNF_E_1),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_7,plain,
( ~ greater(resilience(efficient_producers),resilience(first_movers))
| constant(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T_1),disbanding_rate(efficient_producers,skolemFOFtoCNF_T_1))) ),
inference(resolve,[$cnf( environment(skolemFOFtoCNF_E_1) )],[refute_1_6,refute_1_5]) ).
cnf(refute_1_8,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_9,plain,
constant(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T_1),disbanding_rate(efficient_producers,skolemFOFtoCNF_T_1))),
inference(resolve,[$cnf( greater(resilience(efficient_producers),resilience(first_movers)) )],[refute_1_8,refute_1_7]) ).
cnf(refute_1_10,plain,
decreases(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T_1),disbanding_rate(efficient_producers,skolemFOFtoCNF_T_1))),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_11,plain,
( ~ constant(X)
| ~ decreases(X) ),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_12,plain,
( ~ constant(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T_1),disbanding_rate(efficient_producers,skolemFOFtoCNF_T_1)))
| ~ decreases(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T_1),disbanding_rate(efficient_producers,skolemFOFtoCNF_T_1))) ),
inference(subst,[],[refute_1_11:[bind(X,$fot(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T_1),disbanding_rate(efficient_producers,skolemFOFtoCNF_T_1))))]]) ).
cnf(refute_1_13,plain,
~ constant(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T_1),disbanding_rate(efficient_producers,skolemFOFtoCNF_T_1))),
inference(resolve,[$cnf( decreases(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T_1),disbanding_rate(efficient_producers,skolemFOFtoCNF_T_1))) )],[refute_1_10,refute_1_12]) ).
cnf(refute_1_14,plain,
$false,
inference(resolve,[$cnf( constant(difference(disbanding_rate(first_movers,skolemFOFtoCNF_T_1),disbanding_rate(efficient_producers,skolemFOFtoCNF_T_1))) )],[refute_1_9,refute_1_13]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : MGT022+2 : TPTP v8.1.0. Released v2.0.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jun 9 12:49:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.35
% 0.12/0.35 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------