TSTP Solution File: MGT051-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : MGT051-1 : 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 : n029.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 09:08:40 EDT 2023
% Result : Unsatisfiable 0.63s 0.82s
% Output : CNFRefutation 0.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 45
% Syntax : Number of formulae : 103 ( 25 unt; 21 typ; 0 def)
% Number of atoms : 179 ( 41 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 176 ( 79 ~; 97 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 27 ( 15 >; 12 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 97 ( 12 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
smaller_or_equal: ( $i * $i ) > $o ).
tff(decl_23,type,
smaller: ( $i * $i ) > $o ).
tff(decl_24,type,
greater_or_equal: ( $i * $i ) > $o ).
tff(decl_25,type,
greater: ( $i * $i ) > $o ).
tff(decl_26,type,
has_endowment: $i > $o ).
tff(decl_27,type,
organization: $i > $o ).
tff(decl_28,type,
age: ( $i * $i ) > $i ).
tff(decl_29,type,
eta: $i ).
tff(decl_30,type,
has_immunity: ( $i * $i ) > $o ).
tff(decl_31,type,
sk1: $i > $i ).
tff(decl_32,type,
hazard_of_mortality: ( $i * $i ) > $i ).
tff(decl_33,type,
capability: ( $i * $i ) > $i ).
tff(decl_34,type,
position: ( $i * $i ) > $i ).
tff(decl_35,type,
stock_of_knowledge: ( $i * $i ) > $i ).
tff(decl_36,type,
internal_friction: ( $i * $i ) > $i ).
tff(decl_37,type,
external_ties: ( $i * $i ) > $i ).
tff(decl_38,type,
sk2: $i ).
tff(decl_39,type,
sk3: $i ).
tff(decl_40,type,
sk4: $i ).
tff(decl_41,type,
sk5: $i ).
tff(decl_42,type,
sk6: $i ).
cnf(definition_smaller_or_equal_1,axiom,
( smaller(X1,X2)
| X1 = X2
| ~ smaller_or_equal(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT001-0.ax',definition_smaller_or_equal_1) ).
cnf(theorem_4_63,negated_conjecture,
smaller_or_equal(age(sk2,sk3),age(sk2,sk4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_4_63) ).
cnf(definition_smaller_7,axiom,
( greater(X2,X1)
| ~ smaller(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT001-0.ax',definition_smaller_7) ).
cnf(theorem_4_64,negated_conjecture,
smaller_or_equal(age(sk2,sk4),eta),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_4_64) ).
cnf(meaning_postulate_greater_transitive_10,axiom,
( greater(X1,X3)
| ~ greater(X1,X2)
| ~ greater(X2,X3) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT001-0.ax',meaning_postulate_greater_transitive_10) ).
cnf(assumption_12_60,axiom,
( greater(internal_friction(X1,X2),internal_friction(X1,X3))
| ~ organization(X1)
| ~ greater(age(X1,X2),age(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_12_60) ).
cnf(theorem_4_66,negated_conjecture,
greater(age(sk2,sk6),age(sk2,sk5)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_4_66) ).
cnf(theorem_4_61,negated_conjecture,
organization(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_4_61) ).
cnf(definition_smaller_8,axiom,
( smaller(X2,X1)
| ~ greater(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT001-0.ax',definition_smaller_8) ).
cnf(assumption_5_54,axiom,
( smaller(capability(X1,X2),capability(X1,X3))
| ~ organization(X1)
| ~ smaller_or_equal(stock_of_knowledge(X1,X2),stock_of_knowledge(X1,X3))
| ~ greater(internal_friction(X1,X2),internal_friction(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_5_54) ).
cnf(definition_1_42,axiom,
( has_immunity(X1,X2)
| ~ has_endowment(X1)
| ~ smaller_or_equal(age(X1,X2),eta) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_1_42) ).
cnf(theorem_4_62,negated_conjecture,
has_endowment(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_4_62) ).
cnf(definition_smaller_or_equal_2,axiom,
( smaller_or_equal(X1,X2)
| ~ smaller(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT001-0.ax',definition_smaller_or_equal_2) ).
cnf(assumption_10_58,axiom,
( stock_of_knowledge(X1,X2) = stock_of_knowledge(X1,X3)
| ~ organization(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_10_58) ).
cnf(definition_smaller_or_equal_3,axiom,
( smaller_or_equal(X1,X2)
| X1 != X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT001-0.ax',definition_smaller_or_equal_3) ).
cnf(theorem_4_65,negated_conjecture,
greater(age(sk2,sk5),eta),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_4_65) ).
cnf(assumption_2_48,axiom,
( hazard_of_mortality(X1,X2) = hazard_of_mortality(X1,X3)
| ~ organization(X1)
| ~ has_immunity(X1,X2)
| ~ has_immunity(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_2_48) ).
cnf(definition_1_43,axiom,
( ~ has_endowment(X1)
| ~ greater(age(X1,X2),eta)
| ~ has_immunity(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',definition_1_43) ).
cnf(assumption_4_50,axiom,
( has_immunity(X1,X2)
| has_immunity(X1,X3)
| smaller(hazard_of_mortality(X1,X3),hazard_of_mortality(X1,X2))
| ~ organization(X1)
| ~ greater(capability(X1,X3),capability(X1,X2))
| ~ greater_or_equal(position(X1,X3),position(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_4_50) ).
cnf(assumption_6_57,axiom,
( position(X1,X2) = position(X1,X3)
| ~ organization(X1)
| external_ties(X1,X2) != external_ties(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_6_57) ).
cnf(assumption_11_59,axiom,
( external_ties(X1,X2) = external_ties(X1,X3)
| ~ organization(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_11_59) ).
cnf(assumption_3_49,axiom,
( has_immunity(X1,X3)
| greater(hazard_of_mortality(X1,X3),hazard_of_mortality(X1,X2))
| ~ organization(X1)
| ~ has_immunity(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assumption_3_49) ).
cnf(definition_greater_or_equal_6,axiom,
( greater_or_equal(X1,X2)
| X1 != X2 ),
file('/export/starexec/sandbox/benchmark/Axioms/MGT001-0.ax',definition_greater_or_equal_6) ).
cnf(theorem_4_67,negated_conjecture,
( ~ greater(hazard_of_mortality(sk2,sk6),hazard_of_mortality(sk2,sk5))
| ~ greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk4))
| hazard_of_mortality(sk2,sk4) != hazard_of_mortality(sk2,sk3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_4_67) ).
cnf(c_0_24,axiom,
( smaller(X1,X2)
| X1 = X2
| ~ smaller_or_equal(X1,X2) ),
definition_smaller_or_equal_1 ).
cnf(c_0_25,negated_conjecture,
smaller_or_equal(age(sk2,sk3),age(sk2,sk4)),
theorem_4_63 ).
cnf(c_0_26,axiom,
( greater(X2,X1)
| ~ smaller(X1,X2) ),
definition_smaller_7 ).
cnf(c_0_27,negated_conjecture,
( age(sk2,sk3) = age(sk2,sk4)
| smaller(age(sk2,sk3),age(sk2,sk4)) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
smaller_or_equal(age(sk2,sk4),eta),
theorem_4_64 ).
cnf(c_0_29,axiom,
( greater(X1,X3)
| ~ greater(X1,X2)
| ~ greater(X2,X3) ),
meaning_postulate_greater_transitive_10 ).
cnf(c_0_30,negated_conjecture,
( age(sk2,sk3) = age(sk2,sk4)
| greater(age(sk2,sk4),age(sk2,sk3)) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_31,negated_conjecture,
( age(sk2,sk4) = eta
| smaller(age(sk2,sk4),eta) ),
inference(spm,[status(thm)],[c_0_24,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( age(sk2,sk3) = age(sk2,sk4)
| greater(X1,age(sk2,sk3))
| ~ greater(X1,age(sk2,sk4)) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,negated_conjecture,
( age(sk2,sk4) = eta
| greater(eta,age(sk2,sk4)) ),
inference(spm,[status(thm)],[c_0_26,c_0_31]) ).
cnf(c_0_34,axiom,
( greater(internal_friction(X1,X2),internal_friction(X1,X3))
| ~ organization(X1)
| ~ greater(age(X1,X2),age(X1,X3)) ),
assumption_12_60 ).
cnf(c_0_35,negated_conjecture,
greater(age(sk2,sk6),age(sk2,sk5)),
theorem_4_66 ).
cnf(c_0_36,negated_conjecture,
organization(sk2),
theorem_4_61 ).
cnf(c_0_37,axiom,
( smaller(X2,X1)
| ~ greater(X1,X2) ),
definition_smaller_8 ).
cnf(c_0_38,negated_conjecture,
( age(sk2,sk3) = age(sk2,sk4)
| age(sk2,sk4) = eta
| greater(eta,age(sk2,sk3)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,axiom,
( smaller(capability(X1,X2),capability(X1,X3))
| ~ organization(X1)
| ~ smaller_or_equal(stock_of_knowledge(X1,X2),stock_of_knowledge(X1,X3))
| ~ greater(internal_friction(X1,X2),internal_friction(X1,X3)) ),
assumption_5_54 ).
cnf(c_0_40,negated_conjecture,
greater(internal_friction(sk2,sk6),internal_friction(sk2,sk5)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36])]) ).
cnf(c_0_41,axiom,
( has_immunity(X1,X2)
| ~ has_endowment(X1)
| ~ smaller_or_equal(age(X1,X2),eta) ),
definition_1_42 ).
cnf(c_0_42,negated_conjecture,
has_endowment(sk2),
theorem_4_62 ).
cnf(c_0_43,axiom,
( smaller_or_equal(X1,X2)
| ~ smaller(X1,X2) ),
definition_smaller_or_equal_2 ).
cnf(c_0_44,negated_conjecture,
( age(sk2,sk3) = age(sk2,sk4)
| age(sk2,sk4) = eta
| smaller(age(sk2,sk3),eta) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_45,negated_conjecture,
( smaller(capability(sk2,sk6),capability(sk2,sk5))
| ~ smaller_or_equal(stock_of_knowledge(sk2,sk6),stock_of_knowledge(sk2,sk5)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_36])]) ).
cnf(c_0_46,axiom,
( stock_of_knowledge(X1,X2) = stock_of_knowledge(X1,X3)
| ~ organization(X1) ),
assumption_10_58 ).
cnf(c_0_47,axiom,
( smaller_or_equal(X1,X2)
| X1 != X2 ),
definition_smaller_or_equal_3 ).
cnf(c_0_48,negated_conjecture,
greater(age(sk2,sk5),eta),
theorem_4_65 ).
cnf(c_0_49,axiom,
( hazard_of_mortality(X1,X2) = hazard_of_mortality(X1,X3)
| ~ organization(X1)
| ~ has_immunity(X1,X2)
| ~ has_immunity(X1,X3) ),
assumption_2_48 ).
cnf(c_0_50,negated_conjecture,
has_immunity(sk2,sk4),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_28]),c_0_42])]) ).
cnf(c_0_51,negated_conjecture,
( age(sk2,sk3) = age(sk2,sk4)
| age(sk2,sk4) = eta
| smaller_or_equal(age(sk2,sk3),eta) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_52,negated_conjecture,
( smaller(capability(sk2,sk6),capability(sk2,sk5))
| ~ smaller_or_equal(stock_of_knowledge(sk2,sk6),stock_of_knowledge(sk2,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_36])]) ).
cnf(c_0_53,plain,
smaller_or_equal(X1,X1),
inference(er,[status(thm)],[c_0_47]) ).
cnf(c_0_54,negated_conjecture,
( greater(X1,eta)
| ~ greater(X1,age(sk2,sk5)) ),
inference(spm,[status(thm)],[c_0_29,c_0_48]) ).
cnf(c_0_55,negated_conjecture,
( hazard_of_mortality(sk2,X1) = hazard_of_mortality(sk2,sk4)
| ~ has_immunity(sk2,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_36])]) ).
cnf(c_0_56,negated_conjecture,
( age(sk2,sk3) = age(sk2,sk4)
| age(sk2,sk4) = eta
| has_immunity(sk2,sk3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_51]),c_0_42])]) ).
cnf(c_0_57,negated_conjecture,
smaller(capability(sk2,sk6),capability(sk2,sk5)),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,axiom,
( ~ has_endowment(X1)
| ~ greater(age(X1,X2),eta)
| ~ has_immunity(X1,X2) ),
definition_1_43 ).
cnf(c_0_59,negated_conjecture,
greater(age(sk2,sk6),eta),
inference(spm,[status(thm)],[c_0_54,c_0_35]) ).
cnf(c_0_60,negated_conjecture,
( age(sk2,sk3) = age(sk2,sk4)
| hazard_of_mortality(sk2,sk3) = hazard_of_mortality(sk2,sk4)
| age(sk2,sk4) = eta ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_61,axiom,
( has_immunity(X1,X2)
| has_immunity(X1,X3)
| smaller(hazard_of_mortality(X1,X3),hazard_of_mortality(X1,X2))
| ~ organization(X1)
| ~ greater(capability(X1,X3),capability(X1,X2))
| ~ greater_or_equal(position(X1,X3),position(X1,X2)) ),
assumption_4_50 ).
cnf(c_0_62,negated_conjecture,
greater(capability(sk2,sk5),capability(sk2,sk6)),
inference(spm,[status(thm)],[c_0_26,c_0_57]) ).
cnf(c_0_63,negated_conjecture,
~ has_immunity(sk2,sk5),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_48]),c_0_42])]) ).
cnf(c_0_64,negated_conjecture,
~ has_immunity(sk2,sk6),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_42])]) ).
cnf(c_0_65,axiom,
( position(X1,X2) = position(X1,X3)
| ~ organization(X1)
| external_ties(X1,X2) != external_ties(X1,X3) ),
assumption_6_57 ).
cnf(c_0_66,axiom,
( external_ties(X1,X2) = external_ties(X1,X3)
| ~ organization(X1) ),
assumption_11_59 ).
cnf(c_0_67,axiom,
( has_immunity(X1,X3)
| greater(hazard_of_mortality(X1,X3),hazard_of_mortality(X1,X2))
| ~ organization(X1)
| ~ has_immunity(X1,X2) ),
assumption_3_49 ).
cnf(c_0_68,negated_conjecture,
( hazard_of_mortality(sk2,sk3) = hazard_of_mortality(sk2,sk4)
| age(sk2,sk4) = eta ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_60]),c_0_42]),c_0_28])]),c_0_55]) ).
cnf(c_0_69,negated_conjecture,
( smaller(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk6))
| ~ greater_or_equal(position(sk2,sk5),position(sk2,sk6)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_36])]),c_0_63]),c_0_64]) ).
cnf(c_0_70,plain,
( position(X1,X2) = position(X1,X3)
| ~ organization(X1) ),
inference(csr,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_71,axiom,
( greater_or_equal(X1,X2)
| X1 != X2 ),
definition_greater_or_equal_6 ).
cnf(c_0_72,negated_conjecture,
( ~ greater(hazard_of_mortality(sk2,sk6),hazard_of_mortality(sk2,sk5))
| ~ greater(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk4))
| hazard_of_mortality(sk2,sk4) != hazard_of_mortality(sk2,sk3) ),
theorem_4_67 ).
cnf(c_0_73,negated_conjecture,
( has_immunity(sk2,X1)
| greater(hazard_of_mortality(sk2,X1),hazard_of_mortality(sk2,sk4)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_67,c_0_50]),c_0_36])]) ).
cnf(c_0_74,negated_conjecture,
( hazard_of_mortality(sk2,sk3) = hazard_of_mortality(sk2,sk4)
| smaller_or_equal(age(sk2,sk3),eta) ),
inference(spm,[status(thm)],[c_0_25,c_0_68]) ).
cnf(c_0_75,negated_conjecture,
( smaller(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk6))
| ~ greater_or_equal(position(sk2,sk5),position(sk2,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_36])]) ).
cnf(c_0_76,plain,
greater_or_equal(X1,X1),
inference(er,[status(thm)],[c_0_71]) ).
cnf(c_0_77,negated_conjecture,
( hazard_of_mortality(sk2,sk3) != hazard_of_mortality(sk2,sk4)
| ~ greater(hazard_of_mortality(sk2,sk6),hazard_of_mortality(sk2,sk5)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_63]) ).
cnf(c_0_78,negated_conjecture,
hazard_of_mortality(sk2,sk3) = hazard_of_mortality(sk2,sk4),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_74]),c_0_42])]),c_0_55]) ).
cnf(c_0_79,negated_conjecture,
smaller(hazard_of_mortality(sk2,sk5),hazard_of_mortality(sk2,sk6)),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_80,negated_conjecture,
~ greater(hazard_of_mortality(sk2,sk6),hazard_of_mortality(sk2,sk5)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_77,c_0_78])]) ).
cnf(c_0_81,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_79]),c_0_80]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MGT051-1 : 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
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Aug 28 06:37:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.57 start to proof: theBenchmark
% 0.63/0.82 % Version : CSE_E---1.5
% 0.63/0.82 % Problem : theBenchmark.p
% 0.63/0.82 % Proof found
% 0.63/0.82 % SZS status Theorem for theBenchmark.p
% 0.63/0.82 % SZS output start Proof
% See solution above
% 0.63/0.82 % Total time : 0.238000 s
% 0.63/0.82 % SZS output end Proof
% 0.63/0.82 % Total time : 0.241000 s
%------------------------------------------------------------------------------