%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SEU019+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n009.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 : Tue Jul 19 12:38:08 EDT 2022
% Result : Theorem 0.12s 0.39s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 14
% Syntax : Number of formulae : 94 ( 22 unt; 0 def)
% Number of atoms : 291 ( 96 equ)
% Maximal formula atoms : 23 ( 3 avg)
% Number of connectives : 338 ( 141 ~; 165 |; 22 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 1 con; 0-2 aty)
% Number of variables : 119 ( 5 sgn 38 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d8_funct_1,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ( one_to_one(A)
<=> ! [B,C] :
( ( in(B,relation_dom(A))
& in(C,relation_dom(A))
& apply(A,B) = apply(A,C) )
=> B = C ) ) ) ).
fof(dt_k6_relat_1,axiom,
! [A] : relation(identity_relation(A)) ).
fof(fc2_funct_1,axiom,
! [A] :
( relation(identity_relation(A))
& function(identity_relation(A)) ) ).
fof(t34_funct_1,axiom,
! [A,B] :
( ( relation(B)
& function(B) )
=> ( B = identity_relation(A)
<=> ( relation_dom(B) = A
& ! [C] :
( in(C,A)
=> apply(B,C) = C ) ) ) ) ).
fof(t52_funct_1,conjecture,
! [A] : one_to_one(identity_relation(A)) ).
fof(subgoal_0,plain,
! [A] : one_to_one(identity_relation(A)),
inference(strip,[],[t52_funct_1]) ).
fof(negate_0_0,plain,
~ ! [A] : one_to_one(identity_relation(A)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A] : ~ one_to_one(identity_relation(A)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
~ one_to_one(identity_relation(skolemFOFtoCNF_A_6)),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A] :
( ~ function(A)
| ~ relation(A)
| ( ~ one_to_one(A)
<=> ? [B,C] :
( B != C
& apply(A,B) = apply(A,C)
& in(B,relation_dom(A))
& in(C,relation_dom(A)) ) ) ),
inference(canonicalize,[],[d8_funct_1]) ).
fof(normalize_0_3,plain,
! [A] :
( ~ function(A)
| ~ relation(A)
| ( ~ one_to_one(A)
<=> ? [B,C] :
( B != C
& apply(A,B) = apply(A,C)
& in(B,relation_dom(A))
& in(C,relation_dom(A)) ) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,B,C] :
( ( skolemFOFtoCNF_B(A) != skolemFOFtoCNF_C(A)
| ~ function(A)
| ~ relation(A)
| one_to_one(A) )
& ( ~ function(A)
| ~ relation(A)
| apply(A,skolemFOFtoCNF_B(A)) = apply(A,skolemFOFtoCNF_C(A))
| one_to_one(A) )
& ( ~ function(A)
| ~ relation(A)
| in(skolemFOFtoCNF_B(A),relation_dom(A))
| one_to_one(A) )
& ( ~ function(A)
| ~ relation(A)
| in(skolemFOFtoCNF_C(A),relation_dom(A))
| one_to_one(A) )
& ( apply(A,B) != apply(A,C)
| ~ function(A)
| ~ in(B,relation_dom(A))
| ~ in(C,relation_dom(A))
| ~ one_to_one(A)
| ~ relation(A)
| B = C ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A] :
( skolemFOFtoCNF_B(A) != skolemFOFtoCNF_C(A)
| ~ function(A)
| ~ relation(A)
| one_to_one(A) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,B] :
( ~ function(B)
| ~ relation(B)
| ( B != identity_relation(A)
<=> ( relation_dom(B) != A
| ? [C] :
( apply(B,C) != C
& in(C,A) ) ) ) ),
inference(canonicalize,[],[t34_funct_1]) ).
fof(normalize_0_7,plain,
! [A,B] :
( ~ function(B)
| ~ relation(B)
| ( B != identity_relation(A)
<=> ( relation_dom(B) != A
| ? [C] :
( apply(B,C) != C
& in(C,A) ) ) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B,C] :
( ( B != identity_relation(A)
| ~ function(B)
| ~ relation(B)
| relation_dom(B) = A )
& ( B != identity_relation(A)
| ~ function(B)
| ~ in(C,A)
| ~ relation(B)
| apply(B,C) = C )
& ( apply(B,skolemFOFtoCNF_C_1(A,B)) != skolemFOFtoCNF_C_1(A,B)
| relation_dom(B) != A
| ~ function(B)
| ~ relation(B)
| B = identity_relation(A) )
& ( relation_dom(B) != A
| ~ function(B)
| ~ relation(B)
| B = identity_relation(A)
| in(skolemFOFtoCNF_C_1(A,B),A) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,B,C] :
( B != identity_relation(A)
| ~ function(B)
| ~ in(C,A)
| ~ relation(B)
| apply(B,C) = C ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
( ! [A] : function(identity_relation(A))
& ! [A] : relation(identity_relation(A)) ),
inference(canonicalize,[],[fc2_funct_1]) ).
fof(normalize_0_11,plain,
! [A] : relation(identity_relation(A)),
inference(canonicalize,[],[dt_k6_relat_1]) ).
fof(normalize_0_12,plain,
! [A] : relation(identity_relation(A)),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [A] : function(identity_relation(A)),
inference(simplify,[],[normalize_0_10,normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A] : function(identity_relation(A)),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [A] :
( ~ function(A)
| ~ relation(A)
| in(skolemFOFtoCNF_C(A),relation_dom(A))
| one_to_one(A) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_16,plain,
! [A,B] :
( B != identity_relation(A)
| ~ function(B)
| ~ relation(B)
| relation_dom(B) = A ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_17,plain,
! [A] :
( ~ function(A)
| ~ relation(A)
| apply(A,skolemFOFtoCNF_B(A)) = apply(A,skolemFOFtoCNF_C(A))
| one_to_one(A) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_18,plain,
! [A] :
( ~ function(A)
| ~ relation(A)
| in(skolemFOFtoCNF_B(A),relation_dom(A))
| one_to_one(A) ),
inference(conjunct,[],[normalize_0_4]) ).
cnf(refute_0_0,plain,
~ one_to_one(identity_relation(skolemFOFtoCNF_A_6)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( skolemFOFtoCNF_B(A) != skolemFOFtoCNF_C(A)
| ~ function(A)
| ~ relation(A)
| one_to_one(A) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
( skolemFOFtoCNF_B(identity_relation(X_84)) != skolemFOFtoCNF_C(identity_relation(X_84))
| ~ function(identity_relation(X_84))
| ~ relation(identity_relation(X_84))
| one_to_one(identity_relation(X_84)) ),
inference(subst,[],[refute_0_1:[bind(A,$fot(identity_relation(X_84)))]]) ).
cnf(refute_0_3,plain,
( B != identity_relation(A)
| ~ function(B)
| ~ in(C,A)
| ~ relation(B)
| apply(B,C) = C ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_4,plain,
( identity_relation(A) != identity_relation(A)
| ~ function(identity_relation(A))
| ~ in(C,A)
| ~ relation(identity_relation(A))
| apply(identity_relation(A),C) = C ),
inference(subst,[],[refute_0_3:[bind(B,$fot(identity_relation(A)))]]) ).
cnf(refute_0_5,plain,
identity_relation(A) = identity_relation(A),
introduced(tautology,[refl,[$fot(identity_relation(A))]]) ).
cnf(refute_0_6,plain,
( ~ function(identity_relation(A))
| ~ in(C,A)
| ~ relation(identity_relation(A))
| apply(identity_relation(A),C) = C ),
inference(resolve,[$cnf( $equal(identity_relation(A),identity_relation(A)) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
function(identity_relation(A)),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_8,plain,
( ~ in(C,A)
| ~ relation(identity_relation(A))
| apply(identity_relation(A),C) = C ),
inference(resolve,[$cnf( function(identity_relation(A)) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
relation(identity_relation(A)),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_10,plain,
( ~ in(C,A)
| apply(identity_relation(A),C) = C ),
inference(resolve,[$cnf( relation(identity_relation(A)) )],[refute_0_9,refute_0_8]) ).
cnf(refute_0_11,plain,
( ~ in(skolemFOFtoCNF_C(identity_relation(X_53)),X_53)
| apply(identity_relation(X_53),skolemFOFtoCNF_C(identity_relation(X_53))) = skolemFOFtoCNF_C(identity_relation(X_53)) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(X_53)),bind(C,$fot(skolemFOFtoCNF_C(identity_relation(X_53))))]]) ).
cnf(refute_0_12,plain,
( ~ function(A)
| ~ relation(A)
| in(skolemFOFtoCNF_C(A),relation_dom(A))
| one_to_one(A) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_13,plain,
( ~ function(identity_relation(A))
| ~ relation(identity_relation(A))
| in(skolemFOFtoCNF_C(identity_relation(A)),relation_dom(identity_relation(A)))
| one_to_one(identity_relation(A)) ),
inference(subst,[],[refute_0_12:[bind(A,$fot(identity_relation(A)))]]) ).
cnf(refute_0_14,plain,
( ~ function(identity_relation(A))
| in(skolemFOFtoCNF_C(identity_relation(A)),relation_dom(identity_relation(A)))
| one_to_one(identity_relation(A)) ),
inference(resolve,[$cnf( relation(identity_relation(A)) )],[refute_0_9,refute_0_13]) ).
cnf(refute_0_15,plain,
( B != identity_relation(A)
| ~ function(B)
| ~ relation(B)
| relation_dom(B) = A ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_16,plain,
( identity_relation(A) != identity_relation(A)
| ~ function(identity_relation(A))
| ~ relation(identity_relation(A))
| relation_dom(identity_relation(A)) = A ),
inference(subst,[],[refute_0_15:[bind(B,$fot(identity_relation(A)))]]) ).
cnf(refute_0_17,plain,
( ~ function(identity_relation(A))
| ~ relation(identity_relation(A))
| relation_dom(identity_relation(A)) = A ),
inference(resolve,[$cnf( $equal(identity_relation(A),identity_relation(A)) )],[refute_0_5,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ relation(identity_relation(A))
| relation_dom(identity_relation(A)) = A ),
inference(resolve,[$cnf( function(identity_relation(A)) )],[refute_0_7,refute_0_17]) ).
cnf(refute_0_19,plain,
relation_dom(identity_relation(A)) = A,
inference(resolve,[$cnf( relation(identity_relation(A)) )],[refute_0_9,refute_0_18]) ).
cnf(refute_0_20,plain,
( relation_dom(identity_relation(A)) != A
| ~ in(skolemFOFtoCNF_C(identity_relation(A)),relation_dom(identity_relation(A)))
| in(skolemFOFtoCNF_C(identity_relation(A)),A) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_C(identity_relation(A)),relation_dom(identity_relation(A))) ),[1],$fot(A)]]) ).
cnf(refute_0_21,plain,
( ~ in(skolemFOFtoCNF_C(identity_relation(A)),relation_dom(identity_relation(A)))
| in(skolemFOFtoCNF_C(identity_relation(A)),A) ),
inference(resolve,[$cnf( $equal(relation_dom(identity_relation(A)),A) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ function(identity_relation(A))
| in(skolemFOFtoCNF_C(identity_relation(A)),A)
| one_to_one(identity_relation(A)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(identity_relation(A)),relation_dom(identity_relation(A))) )],[refute_0_14,refute_0_21]) ).
cnf(refute_0_23,plain,
( in(skolemFOFtoCNF_C(identity_relation(A)),A)
| one_to_one(identity_relation(A)) ),
inference(resolve,[$cnf( function(identity_relation(A)) )],[refute_0_7,refute_0_22]) ).
cnf(refute_0_24,plain,
( in(skolemFOFtoCNF_C(identity_relation(X_53)),X_53)
| one_to_one(identity_relation(X_53)) ),
inference(subst,[],[refute_0_23:[bind(A,$fot(X_53))]]) ).
cnf(refute_0_25,plain,
( apply(identity_relation(X_53),skolemFOFtoCNF_C(identity_relation(X_53))) = skolemFOFtoCNF_C(identity_relation(X_53))
| one_to_one(identity_relation(X_53)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_C(identity_relation(X_53)),X_53) )],[refute_0_24,refute_0_11]) ).
cnf(refute_0_26,plain,
( ~ function(A)
| ~ relation(A)
| apply(A,skolemFOFtoCNF_B(A)) = apply(A,skolemFOFtoCNF_C(A))
| one_to_one(A) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_27,plain,
( ~ function(identity_relation(A))
| ~ relation(identity_relation(A))
| apply(identity_relation(A),skolemFOFtoCNF_B(identity_relation(A))) = apply(identity_relation(A),skolemFOFtoCNF_C(identity_relation(A)))
| one_to_one(identity_relation(A)) ),
inference(subst,[],[refute_0_26:[bind(A,$fot(identity_relation(A)))]]) ).
cnf(refute_0_28,plain,
( ~ function(identity_relation(A))
| apply(identity_relation(A),skolemFOFtoCNF_B(identity_relation(A))) = apply(identity_relation(A),skolemFOFtoCNF_C(identity_relation(A)))
| one_to_one(identity_relation(A)) ),
inference(resolve,[$cnf( relation(identity_relation(A)) )],[refute_0_9,refute_0_27]) ).
cnf(refute_0_29,plain,
( apply(identity_relation(A),skolemFOFtoCNF_B(identity_relation(A))) = apply(identity_relation(A),skolemFOFtoCNF_C(identity_relation(A)))
| one_to_one(identity_relation(A)) ),
inference(resolve,[$cnf( function(identity_relation(A)) )],[refute_0_7,refute_0_28]) ).
cnf(refute_0_30,plain,
( apply(identity_relation(X_82),skolemFOFtoCNF_B(identity_relation(X_82))) = apply(identity_relation(X_82),skolemFOFtoCNF_C(identity_relation(X_82)))
| one_to_one(identity_relation(X_82)) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(X_82))]]) ).
cnf(refute_0_31,plain,
( ~ in(skolemFOFtoCNF_B(identity_relation(X_61)),X_61)
| apply(identity_relation(X_61),skolemFOFtoCNF_B(identity_relation(X_61))) = skolemFOFtoCNF_B(identity_relation(X_61)) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(X_61)),bind(C,$fot(skolemFOFtoCNF_B(identity_relation(X_61))))]]) ).
cnf(refute_0_32,plain,
( ~ function(A)
| ~ relation(A)
| in(skolemFOFtoCNF_B(A),relation_dom(A))
| one_to_one(A) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_33,plain,
( ~ function(identity_relation(A))
| ~ relation(identity_relation(A))
| in(skolemFOFtoCNF_B(identity_relation(A)),relation_dom(identity_relation(A)))
| one_to_one(identity_relation(A)) ),
inference(subst,[],[refute_0_32:[bind(A,$fot(identity_relation(A)))]]) ).
cnf(refute_0_34,plain,
( ~ function(identity_relation(A))
| in(skolemFOFtoCNF_B(identity_relation(A)),relation_dom(identity_relation(A)))
| one_to_one(identity_relation(A)) ),
inference(resolve,[$cnf( relation(identity_relation(A)) )],[refute_0_9,refute_0_33]) ).
cnf(refute_0_35,plain,
( relation_dom(identity_relation(A)) != A
| ~ in(skolemFOFtoCNF_B(identity_relation(A)),relation_dom(identity_relation(A)))
| in(skolemFOFtoCNF_B(identity_relation(A)),A) ),
introduced(tautology,[equality,[$cnf( in(skolemFOFtoCNF_B(identity_relation(A)),relation_dom(identity_relation(A))) ),[1],$fot(A)]]) ).
cnf(refute_0_36,plain,
( ~ in(skolemFOFtoCNF_B(identity_relation(A)),relation_dom(identity_relation(A)))
| in(skolemFOFtoCNF_B(identity_relation(A)),A) ),
inference(resolve,[$cnf( $equal(relation_dom(identity_relation(A)),A) )],[refute_0_19,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ function(identity_relation(A))
| in(skolemFOFtoCNF_B(identity_relation(A)),A)
| one_to_one(identity_relation(A)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B(identity_relation(A)),relation_dom(identity_relation(A))) )],[refute_0_34,refute_0_36]) ).
cnf(refute_0_38,plain,
( in(skolemFOFtoCNF_B(identity_relation(A)),A)
| one_to_one(identity_relation(A)) ),
inference(resolve,[$cnf( function(identity_relation(A)) )],[refute_0_7,refute_0_37]) ).
cnf(refute_0_39,plain,
( in(skolemFOFtoCNF_B(identity_relation(X_61)),X_61)
| one_to_one(identity_relation(X_61)) ),
inference(subst,[],[refute_0_38:[bind(A,$fot(X_61))]]) ).
cnf(refute_0_40,plain,
( apply(identity_relation(X_61),skolemFOFtoCNF_B(identity_relation(X_61))) = skolemFOFtoCNF_B(identity_relation(X_61))
| one_to_one(identity_relation(X_61)) ),
inference(resolve,[$cnf( in(skolemFOFtoCNF_B(identity_relation(X_61)),X_61) )],[refute_0_39,refute_0_31]) ).
cnf(refute_0_41,plain,
( apply(identity_relation(X_82),skolemFOFtoCNF_B(identity_relation(X_82))) = skolemFOFtoCNF_B(identity_relation(X_82))
| one_to_one(identity_relation(X_82)) ),
inference(subst,[],[refute_0_40:[bind(X_61,$fot(X_82))]]) ).
cnf(refute_0_42,plain,
( apply(identity_relation(X_82),skolemFOFtoCNF_B(identity_relation(X_82))) != apply(identity_relation(X_82),skolemFOFtoCNF_C(identity_relation(X_82)))
| apply(identity_relation(X_82),skolemFOFtoCNF_B(identity_relation(X_82))) != skolemFOFtoCNF_B(identity_relation(X_82))
| skolemFOFtoCNF_B(identity_relation(X_82)) = apply(identity_relation(X_82),skolemFOFtoCNF_C(identity_relation(X_82))) ),
introduced(tautology,[equality,[$cnf( $equal(apply(identity_relation(X_82),skolemFOFtoCNF_B(identity_relation(X_82))),apply(identity_relation(X_82),skolemFOFtoCNF_C(identity_relation(X_82)))) ),[0],$fot(skolemFOFtoCNF_B(identity_relation(X_82)))]]) ).
cnf(refute_0_43,plain,
( apply(identity_relation(X_82),skolemFOFtoCNF_B(identity_relation(X_82))) != apply(identity_relation(X_82),skolemFOFtoCNF_C(identity_relation(X_82)))
| skolemFOFtoCNF_B(identity_relation(X_82)) = apply(identity_relation(X_82),skolemFOFtoCNF_C(identity_relation(X_82)))
| one_to_one(identity_relation(X_82)) ),
inference(resolve,[$cnf( $equal(apply(identity_relation(X_82),skolemFOFtoCNF_B(identity_relation(X_82))),skolemFOFtoCNF_B(identity_relation(X_82))) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
( skolemFOFtoCNF_B(identity_relation(X_82)) = apply(identity_relation(X_82),skolemFOFtoCNF_C(identity_relation(X_82)))
| one_to_one(identity_relation(X_82)) ),
inference(resolve,[$cnf( $equal(apply(identity_relation(X_82),skolemFOFtoCNF_B(identity_relation(X_82))),apply(identity_relation(X_82),skolemFOFtoCNF_C(identity_relation(X_82)))) )],[refute_0_30,refute_0_43]) ).
cnf(refute_0_45,plain,
( skolemFOFtoCNF_B(identity_relation(X_53)) = apply(identity_relation(X_53),skolemFOFtoCNF_C(identity_relation(X_53)))
| one_to_one(identity_relation(X_53)) ),
inference(subst,[],[refute_0_44:[bind(X_82,$fot(X_53))]]) ).
cnf(refute_0_46,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_47,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_48,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( skolemFOFtoCNF_B(identity_relation(X_53)) != apply(identity_relation(X_53),skolemFOFtoCNF_C(identity_relation(X_53)))
| apply(identity_relation(X_53),skolemFOFtoCNF_C(identity_relation(X_53))) = skolemFOFtoCNF_B(identity_relation(X_53)) ),
inference(subst,[],[refute_0_48:[bind(X,$fot(skolemFOFtoCNF_B(identity_relation(X_53)))),bind(Y,$fot(apply(identity_relation(X_53),skolemFOFtoCNF_C(identity_relation(X_53)))))]]) ).
cnf(refute_0_50,plain,
( apply(identity_relation(X_53),skolemFOFtoCNF_C(identity_relation(X_53))) = skolemFOFtoCNF_B(identity_relation(X_53))
| one_to_one(identity_relation(X_53)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B(identity_relation(X_53)),apply(identity_relation(X_53),skolemFOFtoCNF_C(identity_relation(X_53)))) )],[refute_0_45,refute_0_49]) ).
cnf(refute_0_51,plain,
( apply(identity_relation(X_53),skolemFOFtoCNF_C(identity_relation(X_53))) != skolemFOFtoCNF_B(identity_relation(X_53))
| apply(identity_relation(X_53),skolemFOFtoCNF_C(identity_relation(X_53))) != skolemFOFtoCNF_C(identity_relation(X_53))
| skolemFOFtoCNF_B(identity_relation(X_53)) = skolemFOFtoCNF_C(identity_relation(X_53)) ),
introduced(tautology,[equality,[$cnf( $equal(apply(identity_relation(X_53),skolemFOFtoCNF_C(identity_relation(X_53))),skolemFOFtoCNF_C(identity_relation(X_53))) ),[0],$fot(skolemFOFtoCNF_B(identity_relation(X_53)))]]) ).
cnf(refute_0_52,plain,
( apply(identity_relation(X_53),skolemFOFtoCNF_C(identity_relation(X_53))) != skolemFOFtoCNF_C(identity_relation(X_53))
| skolemFOFtoCNF_B(identity_relation(X_53)) = skolemFOFtoCNF_C(identity_relation(X_53))
| one_to_one(identity_relation(X_53)) ),
inference(resolve,[$cnf( $equal(apply(identity_relation(X_53),skolemFOFtoCNF_C(identity_relation(X_53))),skolemFOFtoCNF_B(identity_relation(X_53))) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( skolemFOFtoCNF_B(identity_relation(X_53)) = skolemFOFtoCNF_C(identity_relation(X_53))
| one_to_one(identity_relation(X_53)) ),
inference(resolve,[$cnf( $equal(apply(identity_relation(X_53),skolemFOFtoCNF_C(identity_relation(X_53))),skolemFOFtoCNF_C(identity_relation(X_53))) )],[refute_0_25,refute_0_52]) ).
cnf(refute_0_54,plain,
( skolemFOFtoCNF_B(identity_relation(X_84)) = skolemFOFtoCNF_C(identity_relation(X_84))
| one_to_one(identity_relation(X_84)) ),
inference(subst,[],[refute_0_53:[bind(X_53,$fot(X_84))]]) ).
cnf(refute_0_55,plain,
( skolemFOFtoCNF_B(identity_relation(X_84)) != skolemFOFtoCNF_C(identity_relation(X_84))
| skolemFOFtoCNF_C(identity_relation(X_84)) = skolemFOFtoCNF_B(identity_relation(X_84)) ),
inference(subst,[],[refute_0_48:[bind(X,$fot(skolemFOFtoCNF_B(identity_relation(X_84)))),bind(Y,$fot(skolemFOFtoCNF_C(identity_relation(X_84))))]]) ).
cnf(refute_0_56,plain,
( skolemFOFtoCNF_C(identity_relation(X_84)) = skolemFOFtoCNF_B(identity_relation(X_84))
| one_to_one(identity_relation(X_84)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B(identity_relation(X_84)),skolemFOFtoCNF_C(identity_relation(X_84))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
( skolemFOFtoCNF_B(identity_relation(X_84)) != skolemFOFtoCNF_B(identity_relation(X_84))
| skolemFOFtoCNF_C(identity_relation(X_84)) != skolemFOFtoCNF_B(identity_relation(X_84))
| skolemFOFtoCNF_B(identity_relation(X_84)) = skolemFOFtoCNF_C(identity_relation(X_84)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(skolemFOFtoCNF_B(identity_relation(X_84)),skolemFOFtoCNF_C(identity_relation(X_84))) ),[1],$fot(skolemFOFtoCNF_B(identity_relation(X_84)))]]) ).
cnf(refute_0_58,plain,
( skolemFOFtoCNF_B(identity_relation(X_84)) != skolemFOFtoCNF_B(identity_relation(X_84))
| skolemFOFtoCNF_B(identity_relation(X_84)) = skolemFOFtoCNF_C(identity_relation(X_84))
| one_to_one(identity_relation(X_84)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_C(identity_relation(X_84)),skolemFOFtoCNF_B(identity_relation(X_84))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( skolemFOFtoCNF_B(identity_relation(X_84)) != skolemFOFtoCNF_B(identity_relation(X_84))
| ~ function(identity_relation(X_84))
| ~ relation(identity_relation(X_84))
| one_to_one(identity_relation(X_84)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B(identity_relation(X_84)),skolemFOFtoCNF_C(identity_relation(X_84))) )],[refute_0_58,refute_0_2]) ).
cnf(refute_0_60,plain,
skolemFOFtoCNF_B(identity_relation(X_84)) = skolemFOFtoCNF_B(identity_relation(X_84)),
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_B(identity_relation(X_84)))]]) ).
cnf(refute_0_61,plain,
( ~ function(identity_relation(X_84))
| ~ relation(identity_relation(X_84))
| one_to_one(identity_relation(X_84)) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_B(identity_relation(X_84)),skolemFOFtoCNF_B(identity_relation(X_84))) )],[refute_0_60,refute_0_59]) ).
cnf(refute_0_62,plain,
function(identity_relation(X_84)),
inference(subst,[],[refute_0_7:[bind(A,$fot(X_84))]]) ).
cnf(refute_0_63,plain,
( ~ relation(identity_relation(X_84))
| one_to_one(identity_relation(X_84)) ),
inference(resolve,[$cnf( function(identity_relation(X_84)) )],[refute_0_62,refute_0_61]) ).
cnf(refute_0_64,plain,
relation(identity_relation(X_84)),
inference(subst,[],[refute_0_9:[bind(A,$fot(X_84))]]) ).
cnf(refute_0_65,plain,
one_to_one(identity_relation(X_84)),
inference(resolve,[$cnf( relation(identity_relation(X_84)) )],[refute_0_64,refute_0_63]) ).
cnf(refute_0_66,plain,
one_to_one(identity_relation(skolemFOFtoCNF_A_6)),
inference(subst,[],[refute_0_65:[bind(X_84,$fot(skolemFOFtoCNF_A_6))]]) ).
cnf(refute_0_67,plain,
$false,
inference(resolve,[$cnf( one_to_one(identity_relation(skolemFOFtoCNF_A_6)) )],[refute_0_66,refute_0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SEU019+1 : TPTP v8.1.0. Released v3.2.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n009.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jun 19 14:15:37 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.39
% 0.12/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.40
%------------------------------------------------------------------------------