TSTP Solution File: MGT027-1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : MGT027-1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n016.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 09:07:25 EDT 2023
% Result : Unsatisfiable 0.21s 0.60s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 32
% Syntax : Number of formulae : 72 ( 7 unt; 16 typ; 0 def)
% Number of atoms : 235 ( 10 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 345 ( 166 ~; 179 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 23 ( 12 >; 11 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 92 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
environment: $i > $o ).
tff(decl_23,type,
stable: $i > $o ).
tff(decl_24,type,
in_environment: ( $i * $i ) > $o ).
tff(decl_25,type,
first_movers: $i ).
tff(decl_26,type,
sk1: ( $i * $i ) > $i ).
tff(decl_27,type,
cardinality_at_time: ( $i * $i ) > $i ).
tff(decl_28,type,
zero: $i ).
tff(decl_29,type,
greater: ( $i * $i ) > $o ).
tff(decl_30,type,
contracts_from: ( $i * $i ) > $o ).
tff(decl_31,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(decl_32,type,
growth_rate: ( $i * $i ) > $i ).
tff(decl_33,type,
efficient_producers: $i ).
tff(decl_34,type,
subpopulations: ( $i * $i * $i * $i ) > $o ).
tff(decl_35,type,
appear: ( $i * $i ) > $i ).
tff(decl_36,type,
sk2: $i > $i ).
tff(decl_37,type,
sk3: $i ).
cnf(mp_greater_transitivity_30,axiom,
( greater(X1,X3)
| ~ greater(X1,X2)
| ~ greater(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_transitivity_30) ).
cnf(l10_35,hypothesis,
( greater(sk2(X1),appear(efficient_producers,X1))
| ~ environment(X1)
| ~ stable(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l10_35) ).
cnf(mp_greater_or_equal_31,axiom,
( greater(X1,X2)
| X1 = X2
| ~ greater_or_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_31) ).
cnf(mp_contracts_from_25,axiom,
( greater_or_equal(sk1(X2,X1),X2)
| contracts_from(X2,first_movers)
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_contracts_from_25) ).
cnf(l10_36,hypothesis,
( greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ stable(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater_or_equal(X2,sk2(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l10_36) ).
cnf(mp_contracts_from_26,axiom,
( contracts_from(X2,first_movers)
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2)
| ~ greater(zero,growth_rate(first_movers,sk1(X2,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_contracts_from_26) ).
cnf(t6_34,hypothesis,
( greater(cardinality_at_time(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater_or_equal(X2,appear(efficient_producers,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_34) ).
cnf(mp_greater_or_equal_32,axiom,
( greater_or_equal(X1,X2)
| ~ greater(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_32) ).
cnf(mp_non_empty_fm_and_ep_27,axiom,
( subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(cardinality_at_time(first_movers,X2),zero)
| ~ greater(cardinality_at_time(efficient_producers,X2),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_non_empty_fm_and_ep_27) ).
cnf(mp_contracts_from_24,axiom,
( greater(cardinality_at_time(first_movers,sk1(X2,X1)),zero)
| contracts_from(X2,first_movers)
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_contracts_from_24) ).
cnf(mp_long_stable_environments_28,axiom,
( in_environment(X1,X3)
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2)
| ~ greater(X3,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_long_stable_environments_28) ).
cnf(mp_greater_or_equal_33,axiom,
( greater_or_equal(X1,X2)
| X1 != X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_33) ).
cnf(mp_EP_in_stable_environments_29,axiom,
( in_environment(X1,appear(efficient_producers,X1))
| ~ environment(X1)
| ~ stable(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_EP_in_stable_environments_29) ).
cnf(prove_l9_39,negated_conjecture,
( ~ greater(X1,appear(efficient_producers,sk3))
| ~ contracts_from(X1,first_movers) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l9_39) ).
cnf(prove_l9_38,negated_conjecture,
stable(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l9_38) ).
cnf(prove_l9_37,negated_conjecture,
environment(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l9_37) ).
cnf(c_0_16,axiom,
( greater(X1,X3)
| ~ greater(X1,X2)
| ~ greater(X2,X3) ),
mp_greater_transitivity_30 ).
cnf(c_0_17,hypothesis,
( greater(sk2(X1),appear(efficient_producers,X1))
| ~ environment(X1)
| ~ stable(X1) ),
l10_35 ).
cnf(c_0_18,axiom,
( greater(X1,X2)
| X1 = X2
| ~ greater_or_equal(X1,X2) ),
mp_greater_or_equal_31 ).
cnf(c_0_19,axiom,
( greater_or_equal(sk1(X2,X1),X2)
| contracts_from(X2,first_movers)
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2) ),
mp_contracts_from_25 ).
cnf(c_0_20,hypothesis,
( greater(zero,growth_rate(first_movers,X2))
| ~ environment(X1)
| ~ stable(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ greater_or_equal(X2,sk2(X1)) ),
l10_36 ).
cnf(c_0_21,axiom,
( contracts_from(X2,first_movers)
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2)
| ~ greater(zero,growth_rate(first_movers,sk1(X2,X1))) ),
mp_contracts_from_26 ).
cnf(c_0_22,hypothesis,
( greater(cardinality_at_time(efficient_producers,X2),zero)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater_or_equal(X2,appear(efficient_producers,X1)) ),
t6_34 ).
cnf(c_0_23,axiom,
( greater_or_equal(X1,X2)
| ~ greater(X1,X2) ),
mp_greater_or_equal_32 ).
cnf(c_0_24,hypothesis,
( greater(X1,appear(efficient_producers,X2))
| ~ greater(X1,sk2(X2))
| ~ stable(X2)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_25,plain,
( sk1(X1,X2) = X1
| contracts_from(X1,first_movers)
| greater(sk1(X1,X2),X1)
| ~ in_environment(X2,X1)
| ~ stable(X2)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_26,hypothesis,
( contracts_from(sk2(X1),first_movers)
| ~ subpopulations(first_movers,efficient_producers,X1,sk1(sk2(X1),X2))
| ~ in_environment(X2,sk2(X1))
| ~ stable(X1)
| ~ stable(X2)
| ~ environment(X1)
| ~ environment(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_19]),c_0_21]) ).
cnf(c_0_27,axiom,
( subpopulations(first_movers,efficient_producers,X1,X2)
| ~ environment(X1)
| ~ in_environment(X1,X2)
| ~ greater(cardinality_at_time(first_movers,X2),zero)
| ~ greater(cardinality_at_time(efficient_producers,X2),zero) ),
mp_non_empty_fm_and_ep_27 ).
cnf(c_0_28,axiom,
( greater(cardinality_at_time(first_movers,sk1(X2,X1)),zero)
| contracts_from(X2,first_movers)
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2) ),
mp_contracts_from_24 ).
cnf(c_0_29,hypothesis,
( greater(cardinality_at_time(efficient_producers,X1),zero)
| ~ greater(X1,appear(efficient_producers,X2))
| ~ in_environment(X2,X1)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_30,hypothesis,
( sk1(sk2(X1),X2) = sk2(X1)
| contracts_from(sk2(X1),first_movers)
| greater(sk1(sk2(X1),X2),appear(efficient_producers,X1))
| ~ in_environment(X2,sk2(X1))
| ~ stable(X1)
| ~ stable(X2)
| ~ environment(X1)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_31,hypothesis,
( contracts_from(sk2(X1),first_movers)
| ~ greater(cardinality_at_time(efficient_producers,sk1(sk2(X1),X2)),zero)
| ~ in_environment(X1,sk1(sk2(X1),X2))
| ~ in_environment(X2,sk2(X1))
| ~ stable(X1)
| ~ stable(X2)
| ~ environment(X1)
| ~ environment(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_32,axiom,
( in_environment(X1,X3)
| ~ environment(X1)
| ~ stable(X1)
| ~ in_environment(X1,X2)
| ~ greater(X3,X2) ),
mp_long_stable_environments_28 ).
cnf(c_0_33,axiom,
( greater_or_equal(X1,X2)
| X1 != X2 ),
mp_greater_or_equal_33 ).
cnf(c_0_34,hypothesis,
( sk1(sk2(X1),X2) = sk2(X1)
| contracts_from(sk2(X1),first_movers)
| ~ in_environment(X1,sk1(sk2(X1),X2))
| ~ in_environment(X2,sk2(X1))
| ~ stable(X1)
| ~ stable(X2)
| ~ environment(X1)
| ~ environment(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).
cnf(c_0_35,plain,
( sk1(X1,X2) = X1
| contracts_from(X1,first_movers)
| in_environment(X3,sk1(X1,X2))
| ~ in_environment(X3,X1)
| ~ in_environment(X2,X1)
| ~ stable(X3)
| ~ stable(X2)
| ~ environment(X3)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_25]) ).
cnf(c_0_36,plain,
greater_or_equal(X1,X1),
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_37,hypothesis,
( greater(cardinality_at_time(efficient_producers,sk2(X1)),zero)
| ~ in_environment(X1,sk2(X1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_17]) ).
cnf(c_0_38,hypothesis,
( in_environment(X1,sk2(X2))
| ~ in_environment(X1,appear(efficient_producers,X2))
| ~ stable(X1)
| ~ stable(X2)
| ~ environment(X1)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_32,c_0_17]) ).
cnf(c_0_39,axiom,
( in_environment(X1,appear(efficient_producers,X1))
| ~ environment(X1)
| ~ stable(X1) ),
mp_EP_in_stable_environments_29 ).
cnf(c_0_40,hypothesis,
( sk1(sk2(X1),X2) = sk2(X1)
| contracts_from(sk2(X1),first_movers)
| ~ in_environment(X2,sk2(X1))
| ~ in_environment(X1,sk2(X1))
| ~ stable(X1)
| ~ stable(X2)
| ~ environment(X1)
| ~ environment(X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,hypothesis,
( greater(zero,growth_rate(first_movers,sk2(X1)))
| ~ subpopulations(first_movers,efficient_producers,X1,sk2(X1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_36]) ).
cnf(c_0_42,hypothesis,
( greater(cardinality_at_time(efficient_producers,sk2(X1)),zero)
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_43,hypothesis,
( sk1(sk2(X1),X2) = sk2(X1)
| contracts_from(sk2(X1),first_movers)
| ~ in_environment(X2,sk2(X1))
| ~ stable(X1)
| ~ stable(X2)
| ~ environment(X1)
| ~ environment(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_38]),c_0_39]) ).
cnf(c_0_44,hypothesis,
( greater(zero,growth_rate(first_movers,sk2(X1)))
| ~ greater(cardinality_at_time(first_movers,sk2(X1)),zero)
| ~ in_environment(X1,sk2(X1))
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_27]),c_0_42]) ).
cnf(c_0_45,hypothesis,
( contracts_from(sk2(X1),first_movers)
| ~ greater(zero,growth_rate(first_movers,sk2(X1)))
| ~ in_environment(X2,sk2(X1))
| ~ stable(X2)
| ~ stable(X1)
| ~ environment(X2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_43]) ).
cnf(c_0_46,hypothesis,
( greater(zero,growth_rate(first_movers,sk2(X1)))
| ~ greater(cardinality_at_time(first_movers,sk2(X1)),zero)
| ~ stable(X1)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_38]),c_0_39]) ).
cnf(c_0_47,hypothesis,
( contracts_from(sk2(X1),first_movers)
| greater(cardinality_at_time(first_movers,sk2(X1)),zero)
| ~ in_environment(X2,sk2(X1))
| ~ stable(X2)
| ~ stable(X1)
| ~ environment(X2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_43]) ).
cnf(c_0_48,hypothesis,
( contracts_from(sk2(X1),first_movers)
| ~ in_environment(X2,sk2(X1))
| ~ stable(X2)
| ~ stable(X1)
| ~ environment(X2)
| ~ environment(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47]) ).
cnf(c_0_49,negated_conjecture,
( ~ greater(X1,appear(efficient_producers,sk3))
| ~ contracts_from(X1,first_movers) ),
prove_l9_39 ).
cnf(c_0_50,negated_conjecture,
stable(sk3),
prove_l9_38 ).
cnf(c_0_51,negated_conjecture,
environment(sk3),
prove_l9_37 ).
cnf(c_0_52,hypothesis,
( contracts_from(sk2(X1),first_movers)
| ~ in_environment(X2,appear(efficient_producers,X1))
| ~ stable(X2)
| ~ stable(X1)
| ~ environment(X2)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_48,c_0_38]) ).
cnf(c_0_53,negated_conjecture,
~ contracts_from(sk2(sk3),first_movers),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_17]),c_0_50]),c_0_51])]) ).
cnf(c_0_54,hypothesis,
( contracts_from(sk2(X1),first_movers)
| ~ stable(X1)
| ~ environment(X1) ),
inference(spm,[status(thm)],[c_0_52,c_0_39]) ).
cnf(c_0_55,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_50]),c_0_51])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : MGT027-1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon Aug 28 06:49:29 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 0.21/0.60 % Version : CSE_E---1.5
% 0.21/0.60 % Problem : theBenchmark.p
% 0.21/0.60 % Proof found
% 0.21/0.60 % SZS status Theorem for theBenchmark.p
% 0.21/0.60 % SZS output start Proof
% See solution above
% 0.21/0.60 % Total time : 0.013000 s
% 0.21/0.60 % SZS output end Proof
% 0.21/0.60 % Total time : 0.016000 s
%------------------------------------------------------------------------------