TSTP Solution File: COL074-3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COL074-3 : TPTP v8.1.0. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 : Fri Jul 15 00:36:26 EDT 2022
% Result : Unsatisfiable 0.20s 0.36s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 42
% Number of leaves : 38
% Syntax : Number of clauses : 108 ( 47 unt; 7 nHn; 84 RR)
% Number of literals : 197 ( 196 equ; 84 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 74 ( 24 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(k_definition,negated_conjecture,
apply(apply(k,X),Y) = X ).
cnf(projection1,axiom,
apply(projection1,pair(X,Y)) = X ).
cnf(projection2,axiom,
apply(projection2,pair(X,Y)) = Y ).
cnf(equality,axiom,
apply(eq,pair(X,X)) = projection1 ).
cnf(extensionality1,axiom,
( X = Y
| apply(eq,pair(X,Y)) = projection2 ) ).
cnf(different_projections,axiom,
projection1 != projection2 ).
cnf(k_projection1,axiom,
apply(k,projection1) = k_projection1 ).
cnf(k_projection2,axiom,
apply(k,projection2) = k_projection2 ).
cnf(self_referential,axiom,
s = apply(eq,pair(apply(k,s),apply(k,projection2))) ).
cnf(refute_0_0,plain,
pair(apply(k,s),apply(k,projection2)) = pair(apply(k,s),apply(k,projection2)),
introduced(tautology,[refl,[$fot(pair(apply(k,s),apply(k,projection2)))]]) ).
cnf(refute_0_1,plain,
( pair(apply(k,s),apply(k,projection2)) != pair(apply(k,s),apply(k,projection2))
| apply(k,projection2) != k_projection2
| pair(apply(k,s),apply(k,projection2)) = pair(apply(k,s),k_projection2) ),
introduced(tautology,[equality,[$cnf( $equal(pair(apply(k,s),apply(k,projection2)),pair(apply(k,s),apply(k,projection2))) ),[1,1],$fot(k_projection2)]]) ).
cnf(refute_0_2,plain,
( apply(k,projection2) != k_projection2
| pair(apply(k,s),apply(k,projection2)) = pair(apply(k,s),k_projection2) ),
inference(resolve,[$cnf( $equal(pair(apply(k,s),apply(k,projection2)),pair(apply(k,s),apply(k,projection2))) )],[refute_0_0,refute_0_1]) ).
cnf(refute_0_3,plain,
pair(apply(k,s),apply(k,projection2)) = pair(apply(k,s),k_projection2),
inference(resolve,[$cnf( $equal(apply(k,projection2),k_projection2) )],[k_projection2,refute_0_2]) ).
cnf(refute_0_4,plain,
apply(eq,pair(apply(k,s),apply(k,projection2))) = apply(eq,pair(apply(k,s),apply(k,projection2))),
introduced(tautology,[refl,[$fot(apply(eq,pair(apply(k,s),apply(k,projection2))))]]) ).
cnf(refute_0_5,plain,
( pair(apply(k,s),apply(k,projection2)) != pair(apply(k,s),k_projection2)
| apply(eq,pair(apply(k,s),apply(k,projection2))) != apply(eq,pair(apply(k,s),apply(k,projection2)))
| apply(eq,pair(apply(k,s),apply(k,projection2))) = apply(eq,pair(apply(k,s),k_projection2)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(eq,pair(apply(k,s),apply(k,projection2))),apply(eq,pair(apply(k,s),apply(k,projection2)))) ),[1,1],$fot(pair(apply(k,s),k_projection2))]]) ).
cnf(refute_0_6,plain,
( pair(apply(k,s),apply(k,projection2)) != pair(apply(k,s),k_projection2)
| apply(eq,pair(apply(k,s),apply(k,projection2))) = apply(eq,pair(apply(k,s),k_projection2)) ),
inference(resolve,[$cnf( $equal(apply(eq,pair(apply(k,s),apply(k,projection2))),apply(eq,pair(apply(k,s),apply(k,projection2)))) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
apply(eq,pair(apply(k,s),apply(k,projection2))) = apply(eq,pair(apply(k,s),k_projection2)),
inference(resolve,[$cnf( $equal(pair(apply(k,s),apply(k,projection2)),pair(apply(k,s),k_projection2)) )],[refute_0_3,refute_0_6]) ).
cnf(refute_0_8,plain,
( apply(eq,pair(apply(k,s),apply(k,projection2))) != apply(eq,pair(apply(k,s),k_projection2))
| s != apply(eq,pair(apply(k,s),apply(k,projection2)))
| s = apply(eq,pair(apply(k,s),k_projection2)) ),
introduced(tautology,[equality,[$cnf( $equal(s,apply(eq,pair(apply(k,s),apply(k,projection2)))) ),[1],$fot(apply(eq,pair(apply(k,s),k_projection2)))]]) ).
cnf(refute_0_9,plain,
( s != apply(eq,pair(apply(k,s),apply(k,projection2)))
| s = apply(eq,pair(apply(k,s),k_projection2)) ),
inference(resolve,[$cnf( $equal(apply(eq,pair(apply(k,s),apply(k,projection2))),apply(eq,pair(apply(k,s),k_projection2))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
s = apply(eq,pair(apply(k,s),k_projection2)),
inference(resolve,[$cnf( $equal(s,apply(eq,pair(apply(k,s),apply(k,projection2)))) )],[self_referential,refute_0_9]) ).
cnf(refute_0_11,plain,
apply(apply(k,s),Y) = s,
inference(subst,[],[k_definition:[bind(X,$fot(s))]]) ).
cnf(refute_0_12,plain,
( apply(eq,pair(apply(k,s),k_projection2)) = projection2
| apply(k,s) = k_projection2 ),
inference(subst,[],[extensionality1:[bind(X,$fot(apply(k,s))),bind(Y,$fot(k_projection2))]]) ).
cnf(refute_0_13,plain,
( apply(eq,pair(apply(k,s),k_projection2)) != projection2
| s != apply(eq,pair(apply(k,s),k_projection2))
| s = projection2 ),
introduced(tautology,[equality,[$cnf( $equal(s,apply(eq,pair(apply(k,s),k_projection2))) ),[1],$fot(projection2)]]) ).
cnf(refute_0_14,plain,
( s != apply(eq,pair(apply(k,s),k_projection2))
| apply(k,s) = k_projection2
| s = projection2 ),
inference(resolve,[$cnf( $equal(apply(eq,pair(apply(k,s),k_projection2)),projection2) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( apply(k,s) = k_projection2
| s = projection2 ),
inference(resolve,[$cnf( $equal(s,apply(eq,pair(apply(k,s),k_projection2))) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
( apply(apply(k,s),Y) != s
| apply(k,s) != k_projection2
| apply(k_projection2,Y) = s ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(k,s),Y),s) ),[0,0],$fot(k_projection2)]]) ).
cnf(refute_0_17,plain,
( apply(apply(k,s),Y) != s
| apply(k_projection2,Y) = s
| s = projection2 ),
inference(resolve,[$cnf( $equal(apply(k,s),k_projection2) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( apply(k_projection2,Y) = s
| s = projection2 ),
inference(resolve,[$cnf( $equal(apply(apply(k,s),Y),s) )],[refute_0_11,refute_0_17]) ).
cnf(refute_0_19,plain,
apply(apply(k,projection2),X_7) = projection2,
inference(subst,[],[k_definition:[bind(X,$fot(projection2)),bind(Y,$fot(X_7))]]) ).
cnf(refute_0_20,plain,
( apply(apply(k,projection2),X_7) != projection2
| apply(k,projection2) != k_projection2
| apply(k_projection2,X_7) = projection2 ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(k,projection2),X_7),projection2) ),[0,0],$fot(k_projection2)]]) ).
cnf(refute_0_21,plain,
( apply(apply(k,projection2),X_7) != projection2
| apply(k_projection2,X_7) = projection2 ),
inference(resolve,[$cnf( $equal(apply(k,projection2),k_projection2) )],[k_projection2,refute_0_20]) ).
cnf(refute_0_22,plain,
apply(k_projection2,X_7) = projection2,
inference(resolve,[$cnf( $equal(apply(apply(k,projection2),X_7),projection2) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
apply(k_projection2,Y) = projection2,
inference(subst,[],[refute_0_22:[bind(X_7,$fot(Y))]]) ).
cnf(refute_0_24,plain,
( apply(k_projection2,Y) != projection2
| apply(k_projection2,Y) != s
| projection2 = s ),
introduced(tautology,[equality,[$cnf( $equal(apply(k_projection2,Y),s) ),[0],$fot(projection2)]]) ).
cnf(refute_0_25,plain,
( apply(k_projection2,Y) != s
| projection2 = s ),
inference(resolve,[$cnf( $equal(apply(k_projection2,Y),projection2) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
( projection2 = s
| s = projection2 ),
inference(resolve,[$cnf( $equal(apply(k_projection2,Y),s) )],[refute_0_18,refute_0_25]) ).
cnf(refute_0_27,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_28,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_29,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
( s != projection2
| projection2 = s ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(s)),bind(Y0,$fot(projection2))]]) ).
cnf(refute_0_31,plain,
projection2 = s,
inference(resolve,[$cnf( $equal(s,projection2) )],[refute_0_26,refute_0_30]) ).
cnf(refute_0_32,plain,
( projection2 != s
| s = projection2 ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(projection2)),bind(Y0,$fot(s))]]) ).
cnf(refute_0_33,plain,
s = projection2,
inference(resolve,[$cnf( $equal(projection2,s) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
( s != apply(eq,pair(apply(k,s),k_projection2))
| s != projection2
| projection2 = apply(eq,pair(apply(k,s),k_projection2)) ),
introduced(tautology,[equality,[$cnf( $equal(s,apply(eq,pair(apply(k,s),k_projection2))) ),[0],$fot(projection2)]]) ).
cnf(refute_0_35,plain,
( s != apply(eq,pair(apply(k,s),k_projection2))
| projection2 = apply(eq,pair(apply(k,s),k_projection2)) ),
inference(resolve,[$cnf( $equal(s,projection2) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
apply(eq,pair(k_projection2,k_projection2)) = projection1,
inference(subst,[],[equality:[bind(X,$fot(k_projection2))]]) ).
cnf(refute_0_37,plain,
apply(k,s) = apply(k,s),
introduced(tautology,[refl,[$fot(apply(k,s))]]) ).
cnf(refute_0_38,plain,
( apply(k,s) != apply(k,s)
| s != projection2
| apply(k,s) = apply(k,projection2) ),
introduced(tautology,[equality,[$cnf( $equal(apply(k,s),apply(k,s)) ),[1,1],$fot(projection2)]]) ).
cnf(refute_0_39,plain,
( s != projection2
| apply(k,s) = apply(k,projection2) ),
inference(resolve,[$cnf( $equal(apply(k,s),apply(k,s)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
apply(k,s) = apply(k,projection2),
inference(resolve,[$cnf( $equal(s,projection2) )],[refute_0_33,refute_0_39]) ).
cnf(refute_0_41,plain,
( Y0 != X0
| Y0 != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_42,plain,
( X0 != Y0
| Y0 != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_29,refute_0_41]) ).
cnf(refute_0_43,plain,
( apply(k,projection2) != k_projection2
| apply(k,s) != apply(k,projection2)
| apply(k,s) = k_projection2 ),
inference(subst,[],[refute_0_42:[bind(X0,$fot(apply(k,s))),bind(Y0,$fot(apply(k,projection2))),bind(Z,$fot(k_projection2))]]) ).
cnf(refute_0_44,plain,
( apply(k,projection2) != k_projection2
| apply(k,s) = k_projection2 ),
inference(resolve,[$cnf( $equal(apply(k,s),apply(k,projection2)) )],[refute_0_40,refute_0_43]) ).
cnf(refute_0_45,plain,
apply(k,s) = k_projection2,
inference(resolve,[$cnf( $equal(apply(k,projection2),k_projection2) )],[k_projection2,refute_0_44]) ).
cnf(refute_0_46,plain,
pair(apply(k,s),k_projection2) = pair(apply(k,s),k_projection2),
introduced(tautology,[refl,[$fot(pair(apply(k,s),k_projection2))]]) ).
cnf(refute_0_47,plain,
( pair(apply(k,s),k_projection2) != pair(apply(k,s),k_projection2)
| apply(k,s) != k_projection2
| pair(apply(k,s),k_projection2) = pair(k_projection2,k_projection2) ),
introduced(tautology,[equality,[$cnf( $equal(pair(apply(k,s),k_projection2),pair(apply(k,s),k_projection2)) ),[1,0],$fot(k_projection2)]]) ).
cnf(refute_0_48,plain,
( apply(k,s) != k_projection2
| pair(apply(k,s),k_projection2) = pair(k_projection2,k_projection2) ),
inference(resolve,[$cnf( $equal(pair(apply(k,s),k_projection2),pair(apply(k,s),k_projection2)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
pair(apply(k,s),k_projection2) = pair(k_projection2,k_projection2),
inference(resolve,[$cnf( $equal(apply(k,s),k_projection2) )],[refute_0_45,refute_0_48]) ).
cnf(refute_0_50,plain,
apply(eq,pair(apply(k,s),k_projection2)) = apply(eq,pair(apply(k,s),k_projection2)),
introduced(tautology,[refl,[$fot(apply(eq,pair(apply(k,s),k_projection2)))]]) ).
cnf(refute_0_51,plain,
( pair(apply(k,s),k_projection2) != pair(k_projection2,k_projection2)
| apply(eq,pair(apply(k,s),k_projection2)) != apply(eq,pair(apply(k,s),k_projection2))
| apply(eq,pair(apply(k,s),k_projection2)) = apply(eq,pair(k_projection2,k_projection2)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(eq,pair(apply(k,s),k_projection2)),apply(eq,pair(apply(k,s),k_projection2))) ),[1,1],$fot(pair(k_projection2,k_projection2))]]) ).
cnf(refute_0_52,plain,
( pair(apply(k,s),k_projection2) != pair(k_projection2,k_projection2)
| apply(eq,pair(apply(k,s),k_projection2)) = apply(eq,pair(k_projection2,k_projection2)) ),
inference(resolve,[$cnf( $equal(apply(eq,pair(apply(k,s),k_projection2)),apply(eq,pair(apply(k,s),k_projection2))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
apply(eq,pair(apply(k,s),k_projection2)) = apply(eq,pair(k_projection2,k_projection2)),
inference(resolve,[$cnf( $equal(pair(apply(k,s),k_projection2),pair(k_projection2,k_projection2)) )],[refute_0_49,refute_0_52]) ).
cnf(refute_0_54,plain,
( apply(eq,pair(apply(k,s),k_projection2)) != apply(eq,pair(k_projection2,k_projection2))
| apply(eq,pair(k_projection2,k_projection2)) != projection1
| apply(eq,pair(apply(k,s),k_projection2)) = projection1 ),
inference(subst,[],[refute_0_42:[bind(X0,$fot(apply(eq,pair(apply(k,s),k_projection2)))),bind(Y0,$fot(apply(eq,pair(k_projection2,k_projection2)))),bind(Z,$fot(projection1))]]) ).
cnf(refute_0_55,plain,
( apply(eq,pair(k_projection2,k_projection2)) != projection1
| apply(eq,pair(apply(k,s),k_projection2)) = projection1 ),
inference(resolve,[$cnf( $equal(apply(eq,pair(apply(k,s),k_projection2)),apply(eq,pair(k_projection2,k_projection2))) )],[refute_0_53,refute_0_54]) ).
cnf(refute_0_56,plain,
apply(eq,pair(apply(k,s),k_projection2)) = projection1,
inference(resolve,[$cnf( $equal(apply(eq,pair(k_projection2,k_projection2)),projection1) )],[refute_0_36,refute_0_55]) ).
cnf(refute_0_57,plain,
( apply(eq,pair(apply(k,s),k_projection2)) != projection1
| projection2 != apply(eq,pair(apply(k,s),k_projection2))
| projection2 = projection1 ),
introduced(tautology,[equality,[$cnf( $equal(projection2,apply(eq,pair(apply(k,s),k_projection2))) ),[1],$fot(projection1)]]) ).
cnf(refute_0_58,plain,
( projection2 != apply(eq,pair(apply(k,s),k_projection2))
| projection2 = projection1 ),
inference(resolve,[$cnf( $equal(apply(eq,pair(apply(k,s),k_projection2)),projection1) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( s != apply(eq,pair(apply(k,s),k_projection2))
| projection2 = projection1 ),
inference(resolve,[$cnf( $equal(projection2,apply(eq,pair(apply(k,s),k_projection2))) )],[refute_0_35,refute_0_58]) ).
cnf(refute_0_60,plain,
projection2 = projection1,
inference(resolve,[$cnf( $equal(s,apply(eq,pair(apply(k,s),k_projection2))) )],[refute_0_10,refute_0_59]) ).
cnf(refute_0_61,plain,
apply(projection2,pair(X,Y)) = apply(projection2,pair(X,Y)),
introduced(tautology,[refl,[$fot(apply(projection2,pair(X,Y)))]]) ).
cnf(refute_0_62,plain,
( apply(projection2,pair(X,Y)) != apply(projection2,pair(X,Y))
| projection2 != projection1
| apply(projection2,pair(X,Y)) = apply(projection1,pair(X,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(projection2,pair(X,Y)),apply(projection2,pair(X,Y))) ),[1,0],$fot(projection1)]]) ).
cnf(refute_0_63,plain,
( projection2 != projection1
| apply(projection2,pair(X,Y)) = apply(projection1,pair(X,Y)) ),
inference(resolve,[$cnf( $equal(apply(projection2,pair(X,Y)),apply(projection2,pair(X,Y))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
apply(projection2,pair(X,Y)) = apply(projection1,pair(X,Y)),
inference(resolve,[$cnf( $equal(projection2,projection1) )],[refute_0_60,refute_0_63]) ).
cnf(refute_0_65,plain,
( apply(projection1,pair(X,Y)) != X
| apply(projection2,pair(X,Y)) != apply(projection1,pair(X,Y))
| apply(projection2,pair(X,Y)) = X ),
inference(subst,[],[refute_0_42:[bind(X0,$fot(apply(projection2,pair(X,Y)))),bind(Y0,$fot(apply(projection1,pair(X,Y)))),bind(Z,$fot(X))]]) ).
cnf(refute_0_66,plain,
( apply(projection1,pair(X,Y)) != X
| apply(projection2,pair(X,Y)) = X ),
inference(resolve,[$cnf( $equal(apply(projection2,pair(X,Y)),apply(projection1,pair(X,Y))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
apply(projection2,pair(X,Y)) = X,
inference(resolve,[$cnf( $equal(apply(projection1,pair(X,Y)),X) )],[projection1,refute_0_66]) ).
cnf(refute_0_68,plain,
( apply(projection2,pair(X,Y)) != X
| apply(projection2,pair(X,Y)) != Y
| X = Y ),
introduced(tautology,[equality,[$cnf( $equal(apply(projection2,pair(X,Y)),Y) ),[0],$fot(X)]]) ).
cnf(refute_0_69,plain,
( apply(projection2,pair(X,Y)) != Y
| X = Y ),
inference(resolve,[$cnf( $equal(apply(projection2,pair(X,Y)),X) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
X = Y,
inference(resolve,[$cnf( $equal(apply(projection2,pair(X,Y)),Y) )],[projection2,refute_0_69]) ).
cnf(refute_0_71,plain,
( X != Y
| Y = X ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(X)),bind(Y0,$fot(Y))]]) ).
cnf(refute_0_72,plain,
Y = X,
inference(resolve,[$cnf( $equal(X,Y) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
apply(eq,pair(X,X)) = X,
inference(subst,[],[refute_0_72:[bind(Y,$fot(apply(eq,pair(X,X))))]]) ).
cnf(refute_0_74,plain,
( apply(eq,pair(X,X)) != X
| apply(eq,pair(X,X)) != projection1
| X = projection1 ),
introduced(tautology,[equality,[$cnf( $equal(apply(eq,pair(X,X)),projection1) ),[0],$fot(X)]]) ).
cnf(refute_0_75,plain,
( apply(eq,pair(X,X)) != projection1
| X = projection1 ),
inference(resolve,[$cnf( $equal(apply(eq,pair(X,X)),X) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
X = projection1,
inference(resolve,[$cnf( $equal(apply(eq,pair(X,X)),projection1) )],[equality,refute_0_75]) ).
cnf(refute_0_77,plain,
apply(k,projection1) = projection1,
inference(subst,[],[refute_0_76:[bind(X,$fot(apply(k,projection1)))]]) ).
cnf(refute_0_78,plain,
( apply(k,projection1) != k_projection1
| apply(k,projection1) != projection1
| projection1 = k_projection1 ),
introduced(tautology,[equality,[$cnf( $equal(apply(k,projection1),k_projection1) ),[0],$fot(projection1)]]) ).
cnf(refute_0_79,plain,
( apply(k,projection1) != k_projection1
| projection1 = k_projection1 ),
inference(resolve,[$cnf( $equal(apply(k,projection1),projection1) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
projection1 = k_projection1,
inference(resolve,[$cnf( $equal(apply(k,projection1),k_projection1) )],[k_projection1,refute_0_79]) ).
cnf(refute_0_81,plain,
( k_projection1 != projection2
| projection1 != k_projection1
| projection1 = projection2 ),
introduced(tautology,[equality,[$cnf( $equal(projection1,k_projection1) ),[1],$fot(projection2)]]) ).
cnf(refute_0_82,plain,
( k_projection1 != projection2
| projection1 = projection2 ),
inference(resolve,[$cnf( $equal(projection1,k_projection1) )],[refute_0_80,refute_0_81]) ).
cnf(refute_0_83,plain,
apply(apply(k,X),Y) = projection1,
inference(subst,[],[refute_0_76:[bind(X,$fot(apply(apply(k,X),Y)))]]) ).
cnf(refute_0_84,plain,
( apply(apply(k,X),Y) != projection1
| projection1 != k_projection1
| apply(apply(k,X),Y) = k_projection1 ),
inference(subst,[],[refute_0_42:[bind(X0,$fot(apply(apply(k,X),Y))),bind(Y0,$fot(projection1)),bind(Z,$fot(k_projection1))]]) ).
cnf(refute_0_85,plain,
( projection1 != k_projection1
| apply(apply(k,X),Y) = k_projection1 ),
inference(resolve,[$cnf( $equal(apply(apply(k,X),Y),projection1) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
apply(apply(k,X),Y) = k_projection1,
inference(resolve,[$cnf( $equal(projection1,k_projection1) )],[refute_0_80,refute_0_85]) ).
cnf(refute_0_87,plain,
( apply(apply(k,X),Y) != X
| apply(apply(k,X),Y) != k_projection1
| k_projection1 = X ),
introduced(tautology,[equality,[$cnf( $equal(apply(apply(k,X),Y),X) ),[0],$fot(k_projection1)]]) ).
cnf(refute_0_88,plain,
( apply(apply(k,X),Y) != X
| k_projection1 = X ),
inference(resolve,[$cnf( $equal(apply(apply(k,X),Y),k_projection1) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
k_projection1 = X,
inference(resolve,[$cnf( $equal(apply(apply(k,X),Y),X) )],[k_definition,refute_0_88]) ).
cnf(refute_0_90,plain,
( k_projection1 != X
| X = k_projection1 ),
inference(subst,[],[refute_0_29:[bind(X0,$fot(k_projection1)),bind(Y0,$fot(X))]]) ).
cnf(refute_0_91,plain,
X = k_projection1,
inference(resolve,[$cnf( $equal(k_projection1,X) )],[refute_0_89,refute_0_90]) ).
cnf(refute_0_92,plain,
projection2 = k_projection1,
inference(subst,[],[refute_0_91:[bind(X,$fot(projection2))]]) ).
cnf(refute_0_93,plain,
( k_projection1 != k_projection1
| projection2 != k_projection1
| k_projection1 = projection2 ),
introduced(tautology,[equality,[$cnf( ~ $equal(k_projection1,projection2) ),[1],$fot(k_projection1)]]) ).
cnf(refute_0_94,plain,
( k_projection1 != k_projection1
| k_projection1 = projection2 ),
inference(resolve,[$cnf( $equal(projection2,k_projection1) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
( k_projection1 != k_projection1
| projection1 = projection2 ),
inference(resolve,[$cnf( $equal(k_projection1,projection2) )],[refute_0_94,refute_0_82]) ).
cnf(refute_0_96,plain,
k_projection1 != k_projection1,
inference(resolve,[$cnf( $equal(projection1,projection2) )],[refute_0_95,different_projections]) ).
cnf(refute_0_97,plain,
k_projection1 = k_projection1,
introduced(tautology,[refl,[$fot(k_projection1)]]) ).
cnf(refute_0_98,plain,
$false,
inference(resolve,[$cnf( $equal(k_projection1,k_projection1) )],[refute_0_97,refute_0_96]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : COL074-3 : TPTP v8.1.0. Released v1.2.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Tue May 31 06:22:44 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.36
% 0.20/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.38
%------------------------------------------------------------------------------