%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT043-1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:16:09 AM UTC 2026
% Result : Unsatisfiable 0.97s 1.20s
% Output : CNFRefutation 0.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 20
% Syntax : Number of clauses : 56 ( 21 unt; 8 nHn; 52 RR)
% Number of literals : 126 ( 35 equ; 61 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(definition_smaller_or_equal_3,axiom,
( A != B
| smaller_or_equal(A,B) ) ).
cnf(definition_greater_or_equal_6,axiom,
( A != B
| greater_or_equal(A,B) ) ).
cnf(definition_smaller_7,axiom,
( ~ smaller(A,B)
| greater(B,A) ) ).
cnf(assumption_4_38,axiom,
( ~ organization(A)
| has_immunity(A,B)
| has_immunity(A,C)
| ~ greater(capability(A,C),capability(A,B))
| ~ greater_or_equal(position(A,C),position(A,B))
| smaller(hazard_of_mortality(A,C),hazard_of_mortality(A,B)) ) ).
cnf(assumption_5_42,axiom,
( ~ organization(A)
| ~ smaller_or_equal(stock_of_knowledge(A,B),stock_of_knowledge(A,C))
| ~ greater(internal_friction(A,B),internal_friction(A,C))
| smaller(capability(A,B),capability(A,C)) ) ).
cnf(assumption_6_45,axiom,
( ~ organization(A)
| external_ties(A,B) != external_ties(A,C)
| position(A,B) = position(A,C) ) ).
cnf(lemma_2_46,negated_conjecture,
organization(sk1) ).
cnf(lemma_2_47,negated_conjecture,
~ has_immunity(sk1,sk2) ).
cnf(lemma_2_48,negated_conjecture,
~ has_immunity(sk1,sk3) ).
cnf(lemma_2_49,negated_conjecture,
stock_of_knowledge(sk1,sk3) = stock_of_knowledge(sk1,sk2) ).
cnf(lemma_2_50,negated_conjecture,
greater(internal_friction(sk1,sk3),internal_friction(sk1,sk2)) ).
cnf(lemma_2_51,negated_conjecture,
external_ties(sk1,sk2) = external_ties(sk1,sk3) ).
cnf(lemma_2_52,negated_conjecture,
~ greater(hazard_of_mortality(sk1,sk3),hazard_of_mortality(sk1,sk2)) ).
cnf(refute_0_0,plain,
( ~ smaller(hazard_of_mortality(sk1,sk2),hazard_of_mortality(sk1,sk3))
| greater(hazard_of_mortality(sk1,sk3),hazard_of_mortality(sk1,sk2)) ),
inference(subst,[],[definition_smaller_7:[bind(A,$fot(hazard_of_mortality(sk1,sk2))),bind(B,$fot(hazard_of_mortality(sk1,sk3)))]]) ).
cnf(refute_0_1,plain,
( B != B
| greater_or_equal(B,B) ),
inference(subst,[],[definition_greater_or_equal_6:[bind(A,$fot(B))]]) ).
cnf(refute_0_2,plain,
B = B,
introduced(tautology,[refl,[$fot(B)]]) ).
cnf(refute_0_3,plain,
greater_or_equal(B,B),
inference(resolve,[$cnf( $equal(B,B) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
greater_or_equal(position(sk1,sk2),position(sk1,sk2)),
inference(subst,[],[refute_0_3:[bind(B,$fot(position(sk1,sk2)))]]) ).
cnf(refute_0_5,plain,
( ~ greater(capability(sk1,X_233),capability(sk1,sk3))
| ~ greater_or_equal(position(sk1,X_233),position(sk1,sk3))
| ~ organization(sk1)
| has_immunity(sk1,X_233)
| has_immunity(sk1,sk3)
| smaller(hazard_of_mortality(sk1,X_233),hazard_of_mortality(sk1,sk3)) ),
inference(subst,[],[assumption_4_38:[bind(A,$fot(sk1)),bind(B,$fot(sk3)),bind(C,$fot(X_233))]]) ).
cnf(refute_0_6,plain,
( external_ties(sk1,sk3) != external_ties(sk1,X_55)
| ~ organization(sk1)
| position(sk1,sk3) = position(sk1,X_55) ),
inference(subst,[],[assumption_6_45:[bind(A,$fot(sk1)),bind(B,$fot(sk3)),bind(C,$fot(X_55))]]) ).
cnf(refute_0_7,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_8,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_9,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
( external_ties(sk1,sk2) != external_ties(sk1,sk3)
| external_ties(sk1,sk3) = external_ties(sk1,sk2) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(external_ties(sk1,sk2))),bind(Y,$fot(external_ties(sk1,sk3)))]]) ).
cnf(refute_0_11,plain,
external_ties(sk1,sk3) = external_ties(sk1,sk2),
inference(resolve,[$cnf( $equal(external_ties(sk1,sk2),external_ties(sk1,sk3)) )],[lemma_2_51,refute_0_10]) ).
cnf(refute_0_12,plain,
( external_ties(sk1,sk2) != external_ties(sk1,X_55)
| external_ties(sk1,sk3) != external_ties(sk1,sk2)
| external_ties(sk1,sk3) = external_ties(sk1,X_55) ),
introduced(tautology,[equality,[$cnf( $equal(external_ties(sk1,sk3),external_ties(sk1,sk2)) ),[1],$fot(external_ties(sk1,X_55))]]) ).
cnf(refute_0_13,plain,
( external_ties(sk1,sk2) != external_ties(sk1,X_55)
| external_ties(sk1,sk3) = external_ties(sk1,X_55) ),
inference(resolve,[$cnf( $equal(external_ties(sk1,sk3),external_ties(sk1,sk2)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( external_ties(sk1,sk2) != external_ties(sk1,X_55)
| ~ organization(sk1)
| position(sk1,sk3) = position(sk1,X_55) ),
inference(resolve,[$cnf( $equal(external_ties(sk1,sk3),external_ties(sk1,X_55)) )],[refute_0_13,refute_0_6]) ).
cnf(refute_0_15,plain,
( external_ties(sk1,sk2) != external_ties(sk1,X_55)
| position(sk1,sk3) = position(sk1,X_55) ),
inference(resolve,[$cnf( organization(sk1) )],[lemma_2_46,refute_0_14]) ).
cnf(refute_0_16,plain,
( external_ties(sk1,sk2) != external_ties(sk1,sk2)
| position(sk1,sk3) = position(sk1,sk2) ),
inference(subst,[],[refute_0_15:[bind(X_55,$fot(sk2))]]) ).
cnf(refute_0_17,plain,
external_ties(sk1,sk2) = external_ties(sk1,sk2),
introduced(tautology,[refl,[$fot(external_ties(sk1,sk2))]]) ).
cnf(refute_0_18,plain,
position(sk1,sk3) = position(sk1,sk2),
inference(resolve,[$cnf( $equal(external_ties(sk1,sk2),external_ties(sk1,sk2)) )],[refute_0_17,refute_0_16]) ).
cnf(refute_0_19,plain,
( position(sk1,sk3) != position(sk1,sk2)
| ~ greater_or_equal(position(sk1,X_233),position(sk1,sk2))
| greater_or_equal(position(sk1,X_233),position(sk1,sk3)) ),
introduced(tautology,[equality,[$cnf( ~ greater_or_equal(position(sk1,X_233),position(sk1,sk3)) ),[1],$fot(position(sk1,sk2))]]) ).
cnf(refute_0_20,plain,
( ~ greater_or_equal(position(sk1,X_233),position(sk1,sk2))
| greater_or_equal(position(sk1,X_233),position(sk1,sk3)) ),
inference(resolve,[$cnf( $equal(position(sk1,sk3),position(sk1,sk2)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ greater(capability(sk1,X_233),capability(sk1,sk3))
| ~ greater_or_equal(position(sk1,X_233),position(sk1,sk2))
| ~ organization(sk1)
| has_immunity(sk1,X_233)
| has_immunity(sk1,sk3)
| smaller(hazard_of_mortality(sk1,X_233),hazard_of_mortality(sk1,sk3)) ),
inference(resolve,[$cnf( greater_or_equal(position(sk1,X_233),position(sk1,sk3)) )],[refute_0_20,refute_0_5]) ).
cnf(refute_0_22,plain,
( ~ greater(capability(sk1,X_233),capability(sk1,sk3))
| ~ greater_or_equal(position(sk1,X_233),position(sk1,sk2))
| has_immunity(sk1,X_233)
| has_immunity(sk1,sk3)
| smaller(hazard_of_mortality(sk1,X_233),hazard_of_mortality(sk1,sk3)) ),
inference(resolve,[$cnf( organization(sk1) )],[lemma_2_46,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ greater(capability(sk1,X_233),capability(sk1,sk3))
| ~ greater_or_equal(position(sk1,X_233),position(sk1,sk2))
| has_immunity(sk1,X_233)
| smaller(hazard_of_mortality(sk1,X_233),hazard_of_mortality(sk1,sk3)) ),
inference(resolve,[$cnf( has_immunity(sk1,sk3) )],[refute_0_22,lemma_2_48]) ).
cnf(refute_0_24,plain,
( ~ greater(capability(sk1,sk2),capability(sk1,sk3))
| ~ greater_or_equal(position(sk1,sk2),position(sk1,sk2))
| has_immunity(sk1,sk2)
| smaller(hazard_of_mortality(sk1,sk2),hazard_of_mortality(sk1,sk3)) ),
inference(subst,[],[refute_0_23:[bind(X_233,$fot(sk2))]]) ).
cnf(refute_0_25,plain,
( ~ greater(capability(sk1,sk2),capability(sk1,sk3))
| has_immunity(sk1,sk2)
| smaller(hazard_of_mortality(sk1,sk2),hazard_of_mortality(sk1,sk3)) ),
inference(resolve,[$cnf( greater_or_equal(position(sk1,sk2),position(sk1,sk2)) )],[refute_0_4,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ smaller(capability(sk1,sk3),capability(sk1,sk2))
| greater(capability(sk1,sk2),capability(sk1,sk3)) ),
inference(subst,[],[definition_smaller_7:[bind(A,$fot(capability(sk1,sk3))),bind(B,$fot(capability(sk1,sk2)))]]) ).
cnf(refute_0_27,plain,
( B != B
| smaller_or_equal(B,B) ),
inference(subst,[],[definition_smaller_or_equal_3:[bind(A,$fot(B))]]) ).
cnf(refute_0_28,plain,
smaller_or_equal(B,B),
inference(resolve,[$cnf( $equal(B,B) )],[refute_0_2,refute_0_27]) ).
cnf(refute_0_29,plain,
smaller_or_equal(stock_of_knowledge(sk1,sk2),stock_of_knowledge(sk1,sk2)),
inference(subst,[],[refute_0_28:[bind(B,$fot(stock_of_knowledge(sk1,sk2)))]]) ).
cnf(refute_0_30,plain,
( ~ greater(internal_friction(sk1,sk3),internal_friction(sk1,X_98))
| ~ organization(sk1)
| ~ smaller_or_equal(stock_of_knowledge(sk1,sk3),stock_of_knowledge(sk1,X_98))
| smaller(capability(sk1,sk3),capability(sk1,X_98)) ),
inference(subst,[],[assumption_5_42:[bind(A,$fot(sk1)),bind(B,$fot(sk3)),bind(C,$fot(X_98))]]) ).
cnf(refute_0_31,plain,
( stock_of_knowledge(sk1,sk3) != stock_of_knowledge(sk1,sk2)
| ~ smaller_or_equal(stock_of_knowledge(sk1,sk2),stock_of_knowledge(sk1,X_98))
| smaller_or_equal(stock_of_knowledge(sk1,sk3),stock_of_knowledge(sk1,X_98)) ),
introduced(tautology,[equality,[$cnf( ~ smaller_or_equal(stock_of_knowledge(sk1,sk3),stock_of_knowledge(sk1,X_98)) ),[0],$fot(stock_of_knowledge(sk1,sk2))]]) ).
cnf(refute_0_32,plain,
( ~ smaller_or_equal(stock_of_knowledge(sk1,sk2),stock_of_knowledge(sk1,X_98))
| smaller_or_equal(stock_of_knowledge(sk1,sk3),stock_of_knowledge(sk1,X_98)) ),
inference(resolve,[$cnf( $equal(stock_of_knowledge(sk1,sk3),stock_of_knowledge(sk1,sk2)) )],[lemma_2_49,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ greater(internal_friction(sk1,sk3),internal_friction(sk1,X_98))
| ~ organization(sk1)
| ~ smaller_or_equal(stock_of_knowledge(sk1,sk2),stock_of_knowledge(sk1,X_98))
| smaller(capability(sk1,sk3),capability(sk1,X_98)) ),
inference(resolve,[$cnf( smaller_or_equal(stock_of_knowledge(sk1,sk3),stock_of_knowledge(sk1,X_98)) )],[refute_0_32,refute_0_30]) ).
cnf(refute_0_34,plain,
( ~ greater(internal_friction(sk1,sk3),internal_friction(sk1,X_98))
| ~ smaller_or_equal(stock_of_knowledge(sk1,sk2),stock_of_knowledge(sk1,X_98))
| smaller(capability(sk1,sk3),capability(sk1,X_98)) ),
inference(resolve,[$cnf( organization(sk1) )],[lemma_2_46,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ greater(internal_friction(sk1,sk3),internal_friction(sk1,sk2))
| ~ smaller_or_equal(stock_of_knowledge(sk1,sk2),stock_of_knowledge(sk1,sk2))
| smaller(capability(sk1,sk3),capability(sk1,sk2)) ),
inference(subst,[],[refute_0_34:[bind(X_98,$fot(sk2))]]) ).
cnf(refute_0_36,plain,
( ~ greater(internal_friction(sk1,sk3),internal_friction(sk1,sk2))
| smaller(capability(sk1,sk3),capability(sk1,sk2)) ),
inference(resolve,[$cnf( smaller_or_equal(stock_of_knowledge(sk1,sk2),stock_of_knowledge(sk1,sk2)) )],[refute_0_29,refute_0_35]) ).
cnf(refute_0_37,plain,
smaller(capability(sk1,sk3),capability(sk1,sk2)),
inference(resolve,[$cnf( greater(internal_friction(sk1,sk3),internal_friction(sk1,sk2)) )],[lemma_2_50,refute_0_36]) ).
cnf(refute_0_38,plain,
greater(capability(sk1,sk2),capability(sk1,sk3)),
inference(resolve,[$cnf( smaller(capability(sk1,sk3),capability(sk1,sk2)) )],[refute_0_37,refute_0_26]) ).
cnf(refute_0_39,plain,
( has_immunity(sk1,sk2)
| smaller(hazard_of_mortality(sk1,sk2),hazard_of_mortality(sk1,sk3)) ),
inference(resolve,[$cnf( greater(capability(sk1,sk2),capability(sk1,sk3)) )],[refute_0_38,refute_0_25]) ).
cnf(refute_0_40,plain,
smaller(hazard_of_mortality(sk1,sk2),hazard_of_mortality(sk1,sk3)),
inference(resolve,[$cnf( has_immunity(sk1,sk2) )],[refute_0_39,lemma_2_47]) ).
cnf(refute_0_41,plain,
greater(hazard_of_mortality(sk1,sk3),hazard_of_mortality(sk1,sk2)),
inference(resolve,[$cnf( smaller(hazard_of_mortality(sk1,sk2),hazard_of_mortality(sk1,sk3)) )],[refute_0_40,refute_0_0]) ).
cnf(refute_0_42,plain,
$false,
inference(resolve,[$cnf( greater(hazard_of_mortality(sk1,sk3),hazard_of_mortality(sk1,sk2)) )],[refute_0_41,lemma_2_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT043-1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.06/0.33 % Computer : n005.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Mon Sep 7 13:06:20 UTC 2026
% 0.06/0.34 % CPUTime :
% 0.06/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.97/1.20 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.97/1.20
% 0.97/1.20 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.97/1.20
%------------------------------------------------------------------------------