TSTP Solution File: SWV236+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWV236+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 : Wed Jul 20 20:30:35 EDT 2022
% Result : Theorem 2.56s 2.72s
% Output : CNFRefutation 2.56s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 28
% Syntax : Number of formulae : 128 ( 67 unt; 0 def)
% Number of atoms : 217 ( 149 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 178 ( 89 ~; 82 |; 5 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 195 ( 0 sgn 35 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(xor_commutative,axiom,
! [X1,X2] : xor(X1,X2) = xor(X2,X1) ).
fof(xor_associative,axiom,
! [X1,X2,X3] : xor(X1,xor(X2,X3)) = xor(xor(X1,X2),X3) ).
fof(xor_rules_1,axiom,
! [X1] : xor(X1,id) = X1 ).
fof(xor_rules_2,axiom,
! [X1] : xor(X1,X1) = id ).
fof(key_part_import___part_1,axiom,
! [Xk,Xtype] :
( ( p(Xk)
& p(Xtype) )
=> p(crypt(xor(km,xor(kp,Xtype)),Xk)) ) ).
fof(combine_with_XOR,axiom,
! [X1,X2] :
( ( p(X1)
& p(X2) )
=> p(xor(X1,X2)) ) ).
fof(initial_knowledge_of_intruder_1,axiom,
p(kp) ).
fof(initial_knowledge_of_intruder_9,axiom,
p(exp) ).
fof(find_known_exporter,conjecture,
? [X] :
( p(crypt(xor(km,exp),X))
& p(X) ) ).
fof(subgoal_0,plain,
? [X] :
( p(crypt(xor(km,exp),X))
& p(X) ),
inference(strip,[],[find_known_exporter]) ).
fof(negate_0_0,plain,
~ ? [X] :
( p(crypt(xor(km,exp),X))
& p(X) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X] :
( ~ p(X)
| ~ p(crypt(xor(km,exp),X)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [X] :
( ~ p(X)
| ~ p(crypt(xor(km,exp),X)) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X1,X2] : xor(X1,X2) = xor(X2,X1),
inference(canonicalize,[],[xor_commutative]) ).
fof(normalize_0_3,plain,
! [X1,X2] : xor(X1,X2) = xor(X2,X1),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [Xk,Xtype] :
( ~ p(Xk)
| ~ p(Xtype)
| p(crypt(xor(km,xor(kp,Xtype)),Xk)) ),
inference(canonicalize,[],[key_part_import___part_1]) ).
fof(normalize_0_5,plain,
! [Xk,Xtype] :
( ~ p(Xk)
| ~ p(Xtype)
| p(crypt(xor(km,xor(kp,Xtype)),Xk)) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
p(kp),
inference(canonicalize,[],[initial_knowledge_of_intruder_1]) ).
fof(normalize_0_7,plain,
p(exp),
inference(canonicalize,[],[initial_knowledge_of_intruder_9]) ).
fof(normalize_0_8,plain,
! [X1,X2] :
( ~ p(X1)
| ~ p(X2)
| p(xor(X1,X2)) ),
inference(canonicalize,[],[combine_with_XOR]) ).
fof(normalize_0_9,plain,
! [X1,X2] :
( ~ p(X1)
| ~ p(X2)
| p(xor(X1,X2)) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X1] : xor(X1,id) = X1,
inference(canonicalize,[],[xor_rules_1]) ).
fof(normalize_0_11,plain,
! [X1] : xor(X1,id) = X1,
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X1] : xor(X1,X1) = id,
inference(canonicalize,[],[xor_rules_2]) ).
fof(normalize_0_13,plain,
! [X1] : xor(X1,X1) = id,
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X1,X2,X3] : xor(X1,xor(X2,X3)) = xor(xor(X1,X2),X3),
inference(canonicalize,[],[xor_associative]) ).
fof(normalize_0_15,plain,
! [X1,X2,X3] : xor(X1,xor(X2,X3)) = xor(xor(X1,X2),X3),
inference(specialize,[],[normalize_0_14]) ).
cnf(refute_0_0,plain,
( ~ p(X)
| ~ p(crypt(xor(km,exp),X)) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
xor(X1,X2) = xor(X2,X1),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_3,plain,
( X0 != X0
| X0 != Y
| Y = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X0 != Y
| Y = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( xor(X1,X2) != xor(X2,X1)
| xor(X2,X1) = xor(X1,X2) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(xor(X1,X2))),bind(Y,$fot(xor(X2,X1)))]]) ).
cnf(refute_0_6,plain,
xor(X2,X1) = xor(X1,X2),
inference(resolve,[$cnf( $equal(xor(X1,X2),xor(X2,X1)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
xor(km,exp) = xor(exp,km),
inference(subst,[],[refute_0_6:[bind(X1,$fot(exp)),bind(X2,$fot(km))]]) ).
cnf(refute_0_8,plain,
crypt(xor(km,exp),X) = crypt(xor(km,exp),X),
introduced(tautology,[refl,[$fot(crypt(xor(km,exp),X))]]) ).
cnf(refute_0_9,plain,
( crypt(xor(km,exp),X) != crypt(xor(km,exp),X)
| xor(km,exp) != xor(exp,km)
| crypt(xor(km,exp),X) = crypt(xor(exp,km),X) ),
introduced(tautology,[equality,[$cnf( $equal(crypt(xor(km,exp),X),crypt(xor(km,exp),X)) ),[1,0],$fot(xor(exp,km))]]) ).
cnf(refute_0_10,plain,
( xor(km,exp) != xor(exp,km)
| crypt(xor(km,exp),X) = crypt(xor(exp,km),X) ),
inference(resolve,[$cnf( $equal(crypt(xor(km,exp),X),crypt(xor(km,exp),X)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
crypt(xor(km,exp),X) = crypt(xor(exp,km),X),
inference(resolve,[$cnf( $equal(xor(km,exp),xor(exp,km)) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
( crypt(xor(km,exp),X) != crypt(xor(exp,km),X)
| ~ p(crypt(xor(exp,km),X))
| p(crypt(xor(km,exp),X)) ),
introduced(tautology,[equality,[$cnf( ~ p(crypt(xor(km,exp),X)) ),[0],$fot(crypt(xor(exp,km),X))]]) ).
cnf(refute_0_13,plain,
( ~ p(crypt(xor(exp,km),X))
| p(crypt(xor(km,exp),X)) ),
inference(resolve,[$cnf( $equal(crypt(xor(km,exp),X),crypt(xor(exp,km),X)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ p(X)
| ~ p(crypt(xor(exp,km),X)) ),
inference(resolve,[$cnf( p(crypt(xor(km,exp),X)) )],[refute_0_13,refute_0_0]) ).
cnf(refute_0_15,plain,
( ~ p(crypt(xor(exp,km),xor(exp,kp)))
| ~ p(xor(exp,kp)) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(xor(exp,kp)))]]) ).
cnf(refute_0_16,plain,
( ~ p(Xk)
| ~ p(Xtype)
| p(crypt(xor(km,xor(kp,Xtype)),Xk)) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_17,plain,
( ~ p(xor(exp,kp))
| p(crypt(xor(km,xor(kp,xor(exp,kp))),xor(exp,kp))) ),
inference(subst,[],[refute_0_16:[bind(Xk,$fot(xor(exp,kp))),bind(Xtype,$fot(xor(exp,kp)))]]) ).
cnf(refute_0_18,plain,
p(kp),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_19,plain,
p(exp),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_20,plain,
( ~ p(X1)
| ~ p(X2)
| p(xor(X1,X2)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_21,plain,
( ~ p(X_48)
| ~ p(exp)
| p(xor(exp,X_48)) ),
inference(subst,[],[refute_0_20:[bind(X1,$fot(exp)),bind(X2,$fot(X_48))]]) ).
cnf(refute_0_22,plain,
( ~ p(X_48)
| p(xor(exp,X_48)) ),
inference(resolve,[$cnf( p(exp) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ p(kp)
| p(xor(exp,kp)) ),
inference(subst,[],[refute_0_22:[bind(X_48,$fot(kp))]]) ).
cnf(refute_0_24,plain,
p(xor(exp,kp)),
inference(resolve,[$cnf( p(kp) )],[refute_0_18,refute_0_23]) ).
cnf(refute_0_25,plain,
p(crypt(xor(km,xor(kp,xor(exp,kp))),xor(exp,kp))),
inference(resolve,[$cnf( p(xor(exp,kp)) )],[refute_0_24,refute_0_17]) ).
cnf(refute_0_26,plain,
xor(X1,id) = X1,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_27,plain,
xor(km,id) = km,
inference(subst,[],[refute_0_26:[bind(X1,$fot(km))]]) ).
cnf(refute_0_28,plain,
xor(X1,X1) = id,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_29,plain,
xor(kp,kp) = id,
inference(subst,[],[refute_0_28:[bind(X1,$fot(kp))]]) ).
cnf(refute_0_30,plain,
xor(km,xor(kp,kp)) = xor(km,xor(kp,kp)),
introduced(tautology,[refl,[$fot(xor(km,xor(kp,kp)))]]) ).
cnf(refute_0_31,plain,
( xor(km,xor(kp,kp)) != xor(km,xor(kp,kp))
| xor(kp,kp) != id
| xor(km,xor(kp,kp)) = xor(km,id) ),
introduced(tautology,[equality,[$cnf( $equal(xor(km,xor(kp,kp)),xor(km,xor(kp,kp))) ),[1,1],$fot(id)]]) ).
cnf(refute_0_32,plain,
( xor(kp,kp) != id
| xor(km,xor(kp,kp)) = xor(km,id) ),
inference(resolve,[$cnf( $equal(xor(km,xor(kp,kp)),xor(km,xor(kp,kp))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
xor(km,xor(kp,kp)) = xor(km,id),
inference(resolve,[$cnf( $equal(xor(kp,kp),id) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
( Y != X0
| Y != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_35,plain,
( X0 != Y
| Y != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y,X0) )],[refute_0_4,refute_0_34]) ).
cnf(refute_0_36,plain,
( xor(km,id) != km
| xor(km,xor(kp,kp)) != xor(km,id)
| xor(km,xor(kp,kp)) = km ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(xor(km,xor(kp,kp)))),bind(Y,$fot(xor(km,id))),bind(Z,$fot(km))]]) ).
cnf(refute_0_37,plain,
( xor(km,id) != km
| xor(km,xor(kp,kp)) = km ),
inference(resolve,[$cnf( $equal(xor(km,xor(kp,kp)),xor(km,id)) )],[refute_0_33,refute_0_36]) ).
cnf(refute_0_38,plain,
xor(km,xor(kp,kp)) = km,
inference(resolve,[$cnf( $equal(xor(km,id),km) )],[refute_0_27,refute_0_37]) ).
cnf(refute_0_39,plain,
xor(exp,xor(km,xor(kp,kp))) = xor(exp,xor(km,xor(kp,kp))),
introduced(tautology,[refl,[$fot(xor(exp,xor(km,xor(kp,kp))))]]) ).
cnf(refute_0_40,plain,
( xor(exp,xor(km,xor(kp,kp))) != xor(exp,xor(km,xor(kp,kp)))
| xor(km,xor(kp,kp)) != km
| xor(exp,xor(km,xor(kp,kp))) = xor(exp,km) ),
introduced(tautology,[equality,[$cnf( $equal(xor(exp,xor(km,xor(kp,kp))),xor(exp,xor(km,xor(kp,kp)))) ),[1,1],$fot(km)]]) ).
cnf(refute_0_41,plain,
( xor(km,xor(kp,kp)) != km
| xor(exp,xor(km,xor(kp,kp))) = xor(exp,km) ),
inference(resolve,[$cnf( $equal(xor(exp,xor(km,xor(kp,kp))),xor(exp,xor(km,xor(kp,kp)))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
xor(exp,xor(km,xor(kp,kp))) = xor(exp,km),
inference(resolve,[$cnf( $equal(xor(km,xor(kp,kp)),km) )],[refute_0_38,refute_0_41]) ).
cnf(refute_0_43,plain,
xor(X1,xor(X2,X3)) = xor(xor(X1,X2),X3),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_44,plain,
xor(X1,xor(X2,xor(X_25,X_26))) = xor(xor(X1,X2),xor(X_25,X_26)),
inference(subst,[],[refute_0_43:[bind(X3,$fot(xor(X_25,X_26)))]]) ).
cnf(refute_0_45,plain,
xor(X_9,xor(X_10,X_11)) = xor(xor(X_9,X_10),X_11),
inference(subst,[],[refute_0_43:[bind(X1,$fot(X_9)),bind(X2,$fot(X_10)),bind(X3,$fot(X_11))]]) ).
cnf(refute_0_46,plain,
xor(X_10,X_9) = xor(X_9,X_10),
inference(subst,[],[refute_0_1:[bind(X1,$fot(X_10)),bind(X2,$fot(X_9))]]) ).
cnf(refute_0_47,plain,
( xor(X_10,X_9) != xor(X_9,X_10)
| xor(X_9,X_10) = xor(X_10,X_9) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(xor(X_10,X_9))),bind(Y,$fot(xor(X_9,X_10)))]]) ).
cnf(refute_0_48,plain,
xor(X_9,X_10) = xor(X_10,X_9),
inference(resolve,[$cnf( $equal(xor(X_10,X_9),xor(X_9,X_10)) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
( xor(X_9,X_10) != xor(X_10,X_9)
| xor(X_9,xor(X_10,X_11)) != xor(xor(X_9,X_10),X_11)
| xor(X_9,xor(X_10,X_11)) = xor(xor(X_10,X_9),X_11) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_9,xor(X_10,X_11)),xor(xor(X_9,X_10),X_11)) ),[1,0],$fot(xor(X_10,X_9))]]) ).
cnf(refute_0_50,plain,
( xor(X_9,xor(X_10,X_11)) != xor(xor(X_9,X_10),X_11)
| xor(X_9,xor(X_10,X_11)) = xor(xor(X_10,X_9),X_11) ),
inference(resolve,[$cnf( $equal(xor(X_9,X_10),xor(X_10,X_9)) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
xor(X_9,xor(X_10,X_11)) = xor(xor(X_10,X_9),X_11),
inference(resolve,[$cnf( $equal(xor(X_9,xor(X_10,X_11)),xor(xor(X_9,X_10),X_11)) )],[refute_0_45,refute_0_50]) ).
cnf(refute_0_52,plain,
( xor(X1,xor(X2,X3)) != xor(xor(X1,X2),X3)
| xor(xor(X1,X2),X3) = xor(X1,xor(X2,X3)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(xor(X1,xor(X2,X3)))),bind(Y,$fot(xor(xor(X1,X2),X3)))]]) ).
cnf(refute_0_53,plain,
xor(xor(X1,X2),X3) = xor(X1,xor(X2,X3)),
inference(resolve,[$cnf( $equal(xor(X1,xor(X2,X3)),xor(xor(X1,X2),X3)) )],[refute_0_43,refute_0_52]) ).
cnf(refute_0_54,plain,
xor(xor(X_10,X_9),X_11) = xor(X_10,xor(X_9,X_11)),
inference(subst,[],[refute_0_53:[bind(X1,$fot(X_10)),bind(X2,$fot(X_9)),bind(X3,$fot(X_11))]]) ).
cnf(refute_0_55,plain,
( xor(X_9,xor(X_10,X_11)) != xor(xor(X_10,X_9),X_11)
| xor(xor(X_10,X_9),X_11) != xor(X_10,xor(X_9,X_11))
| xor(X_9,xor(X_10,X_11)) = xor(X_10,xor(X_9,X_11)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(xor(X_9,xor(X_10,X_11)),xor(X_10,xor(X_9,X_11))) ),[0],$fot(xor(xor(X_10,X_9),X_11))]]) ).
cnf(refute_0_56,plain,
( xor(X_9,xor(X_10,X_11)) != xor(xor(X_10,X_9),X_11)
| xor(X_9,xor(X_10,X_11)) = xor(X_10,xor(X_9,X_11)) ),
inference(resolve,[$cnf( $equal(xor(xor(X_10,X_9),X_11),xor(X_10,xor(X_9,X_11))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
xor(X_9,xor(X_10,X_11)) = xor(X_10,xor(X_9,X_11)),
inference(resolve,[$cnf( $equal(xor(X_9,xor(X_10,X_11)),xor(xor(X_10,X_9),X_11)) )],[refute_0_51,refute_0_56]) ).
cnf(refute_0_58,plain,
xor(X2,xor(X_25,X_26)) = xor(X_25,xor(X2,X_26)),
inference(subst,[],[refute_0_57:[bind(X_10,$fot(X_25)),bind(X_11,$fot(X_26)),bind(X_9,$fot(X2))]]) ).
cnf(refute_0_59,plain,
( xor(X1,xor(X2,xor(X_25,X_26))) != xor(xor(X1,X2),xor(X_25,X_26))
| xor(X2,xor(X_25,X_26)) != xor(X_25,xor(X2,X_26))
| xor(X1,xor(X_25,xor(X2,X_26))) = xor(xor(X1,X2),xor(X_25,X_26)) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X1,xor(X2,xor(X_25,X_26))),xor(xor(X1,X2),xor(X_25,X_26))) ),[0,1],$fot(xor(X_25,xor(X2,X_26)))]]) ).
cnf(refute_0_60,plain,
( xor(X1,xor(X2,xor(X_25,X_26))) != xor(xor(X1,X2),xor(X_25,X_26))
| xor(X1,xor(X_25,xor(X2,X_26))) = xor(xor(X1,X2),xor(X_25,X_26)) ),
inference(resolve,[$cnf( $equal(xor(X2,xor(X_25,X_26)),xor(X_25,xor(X2,X_26))) )],[refute_0_58,refute_0_59]) ).
cnf(refute_0_61,plain,
xor(X1,xor(X_25,xor(X2,X_26))) = xor(xor(X1,X2),xor(X_25,X_26)),
inference(resolve,[$cnf( $equal(xor(X1,xor(X2,xor(X_25,X_26))),xor(xor(X1,X2),xor(X_25,X_26))) )],[refute_0_44,refute_0_60]) ).
cnf(refute_0_62,plain,
xor(xor(X1,X2),xor(X_25,X_26)) = xor(X1,xor(X2,xor(X_25,X_26))),
inference(subst,[],[refute_0_53:[bind(X3,$fot(xor(X_25,X_26)))]]) ).
cnf(refute_0_63,plain,
( xor(X1,xor(X_25,xor(X2,X_26))) != xor(xor(X1,X2),xor(X_25,X_26))
| xor(xor(X1,X2),xor(X_25,X_26)) != xor(X1,xor(X2,xor(X_25,X_26)))
| xor(X1,xor(X_25,xor(X2,X_26))) = xor(X1,xor(X2,xor(X_25,X_26))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(xor(X1,xor(X_25,xor(X2,X_26))),xor(X1,xor(X2,xor(X_25,X_26)))) ),[0],$fot(xor(xor(X1,X2),xor(X_25,X_26)))]]) ).
cnf(refute_0_64,plain,
( xor(X1,xor(X_25,xor(X2,X_26))) != xor(xor(X1,X2),xor(X_25,X_26))
| xor(X1,xor(X_25,xor(X2,X_26))) = xor(X1,xor(X2,xor(X_25,X_26))) ),
inference(resolve,[$cnf( $equal(xor(xor(X1,X2),xor(X_25,X_26)),xor(X1,xor(X2,xor(X_25,X_26)))) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
xor(X1,xor(X_25,xor(X2,X_26))) = xor(X1,xor(X2,xor(X_25,X_26))),
inference(resolve,[$cnf( $equal(xor(X1,xor(X_25,xor(X2,X_26))),xor(xor(X1,X2),xor(X_25,X_26))) )],[refute_0_61,refute_0_64]) ).
cnf(refute_0_66,plain,
xor(X_43,xor(X_45,xor(X_44,X_46))) = xor(X_43,xor(X_44,xor(X_45,X_46))),
inference(subst,[],[refute_0_65:[bind(X1,$fot(X_43)),bind(X2,$fot(X_44)),bind(X_25,$fot(X_45)),bind(X_26,$fot(X_46))]]) ).
cnf(refute_0_67,plain,
xor(X_46,X_44) = xor(X_44,X_46),
inference(subst,[],[refute_0_1:[bind(X1,$fot(X_46)),bind(X2,$fot(X_44))]]) ).
cnf(refute_0_68,plain,
( xor(X_46,X_44) != xor(X_44,X_46)
| xor(X_44,X_46) = xor(X_46,X_44) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(xor(X_46,X_44))),bind(Y,$fot(xor(X_44,X_46)))]]) ).
cnf(refute_0_69,plain,
xor(X_44,X_46) = xor(X_46,X_44),
inference(resolve,[$cnf( $equal(xor(X_46,X_44),xor(X_44,X_46)) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
( xor(X_43,xor(X_45,xor(X_44,X_46))) != xor(X_43,xor(X_44,xor(X_45,X_46)))
| xor(X_44,X_46) != xor(X_46,X_44)
| xor(X_43,xor(X_45,xor(X_46,X_44))) = xor(X_43,xor(X_44,xor(X_45,X_46))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_43,xor(X_45,xor(X_44,X_46))),xor(X_43,xor(X_44,xor(X_45,X_46)))) ),[0,1,1],$fot(xor(X_46,X_44))]]) ).
cnf(refute_0_71,plain,
( xor(X_43,xor(X_45,xor(X_44,X_46))) != xor(X_43,xor(X_44,xor(X_45,X_46)))
| xor(X_43,xor(X_45,xor(X_46,X_44))) = xor(X_43,xor(X_44,xor(X_45,X_46))) ),
inference(resolve,[$cnf( $equal(xor(X_44,X_46),xor(X_46,X_44)) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
xor(X_43,xor(X_45,xor(X_46,X_44))) = xor(X_43,xor(X_44,xor(X_45,X_46))),
inference(resolve,[$cnf( $equal(xor(X_43,xor(X_45,xor(X_44,X_46))),xor(X_43,xor(X_44,xor(X_45,X_46)))) )],[refute_0_66,refute_0_71]) ).
cnf(refute_0_73,plain,
( xor(X_43,xor(X_45,xor(X_46,X_44))) != xor(X_43,xor(X_44,xor(X_45,X_46)))
| xor(X_43,xor(X_44,xor(X_45,X_46))) = xor(X_43,xor(X_45,xor(X_46,X_44))) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(xor(X_43,xor(X_45,xor(X_46,X_44))))),bind(Y,$fot(xor(X_43,xor(X_44,xor(X_45,X_46)))))]]) ).
cnf(refute_0_74,plain,
xor(X_43,xor(X_44,xor(X_45,X_46))) = xor(X_43,xor(X_45,xor(X_46,X_44))),
inference(resolve,[$cnf( $equal(xor(X_43,xor(X_45,xor(X_46,X_44))),xor(X_43,xor(X_44,xor(X_45,X_46)))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
xor(exp,xor(kp,xor(km,kp))) = xor(exp,xor(km,xor(kp,kp))),
inference(subst,[],[refute_0_74:[bind(X_43,$fot(exp)),bind(X_44,$fot(kp)),bind(X_45,$fot(km)),bind(X_46,$fot(kp))]]) ).
cnf(refute_0_76,plain,
xor(X_9,xor(X_10,xor(X_44,X_46))) = xor(X_10,xor(X_9,xor(X_44,X_46))),
inference(subst,[],[refute_0_57:[bind(X_11,$fot(xor(X_44,X_46)))]]) ).
cnf(refute_0_77,plain,
xor(X_10,xor(X_9,xor(X_44,X_46))) = xor(X_10,xor(X_44,xor(X_9,X_46))),
inference(subst,[],[refute_0_65:[bind(X1,$fot(X_10)),bind(X2,$fot(X_44)),bind(X_25,$fot(X_9)),bind(X_26,$fot(X_46))]]) ).
cnf(refute_0_78,plain,
( xor(X_10,xor(X_9,xor(X_44,X_46))) != xor(X_10,xor(X_44,xor(X_9,X_46)))
| xor(X_9,xor(X_10,xor(X_44,X_46))) != xor(X_10,xor(X_9,xor(X_44,X_46)))
| xor(X_9,xor(X_10,xor(X_44,X_46))) = xor(X_10,xor(X_44,xor(X_9,X_46))) ),
introduced(tautology,[equality,[$cnf( $equal(xor(X_9,xor(X_10,xor(X_44,X_46))),xor(X_10,xor(X_9,xor(X_44,X_46)))) ),[1],$fot(xor(X_10,xor(X_44,xor(X_9,X_46))))]]) ).
cnf(refute_0_79,plain,
( xor(X_9,xor(X_10,xor(X_44,X_46))) != xor(X_10,xor(X_9,xor(X_44,X_46)))
| xor(X_9,xor(X_10,xor(X_44,X_46))) = xor(X_10,xor(X_44,xor(X_9,X_46))) ),
inference(resolve,[$cnf( $equal(xor(X_10,xor(X_9,xor(X_44,X_46))),xor(X_10,xor(X_44,xor(X_9,X_46)))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
xor(X_9,xor(X_10,xor(X_44,X_46))) = xor(X_10,xor(X_44,xor(X_9,X_46))),
inference(resolve,[$cnf( $equal(xor(X_9,xor(X_10,xor(X_44,X_46))),xor(X_10,xor(X_9,xor(X_44,X_46)))) )],[refute_0_76,refute_0_79]) ).
cnf(refute_0_81,plain,
xor(km,xor(exp,xor(kp,kp))) = xor(exp,xor(kp,xor(km,kp))),
inference(subst,[],[refute_0_80:[bind(X_10,$fot(exp)),bind(X_44,$fot(kp)),bind(X_46,$fot(kp)),bind(X_9,$fot(km))]]) ).
cnf(refute_0_82,plain,
( xor(exp,xor(kp,xor(km,kp))) != xor(exp,xor(km,xor(kp,kp)))
| xor(km,xor(exp,xor(kp,kp))) != xor(exp,xor(kp,xor(km,kp)))
| xor(km,xor(exp,xor(kp,kp))) = xor(exp,xor(km,xor(kp,kp))) ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(xor(km,xor(exp,xor(kp,kp))))),bind(Y,$fot(xor(exp,xor(kp,xor(km,kp))))),bind(Z,$fot(xor(exp,xor(km,xor(kp,kp)))))]]) ).
cnf(refute_0_83,plain,
( xor(exp,xor(kp,xor(km,kp))) != xor(exp,xor(km,xor(kp,kp)))
| xor(km,xor(exp,xor(kp,kp))) = xor(exp,xor(km,xor(kp,kp))) ),
inference(resolve,[$cnf( $equal(xor(km,xor(exp,xor(kp,kp))),xor(exp,xor(kp,xor(km,kp)))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
xor(km,xor(exp,xor(kp,kp))) = xor(exp,xor(km,xor(kp,kp))),
inference(resolve,[$cnf( $equal(xor(exp,xor(kp,xor(km,kp))),xor(exp,xor(km,xor(kp,kp)))) )],[refute_0_75,refute_0_83]) ).
cnf(refute_0_85,plain,
xor(km,xor(kp,xor(exp,kp))) = xor(km,xor(exp,xor(kp,kp))),
inference(subst,[],[refute_0_74:[bind(X_43,$fot(km)),bind(X_44,$fot(kp)),bind(X_45,$fot(exp)),bind(X_46,$fot(kp))]]) ).
cnf(refute_0_86,plain,
( xor(km,xor(exp,xor(kp,kp))) != xor(exp,xor(km,xor(kp,kp)))
| xor(km,xor(kp,xor(exp,kp))) != xor(km,xor(exp,xor(kp,kp)))
| xor(km,xor(kp,xor(exp,kp))) = xor(exp,xor(km,xor(kp,kp))) ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(xor(km,xor(kp,xor(exp,kp))))),bind(Y,$fot(xor(km,xor(exp,xor(kp,kp))))),bind(Z,$fot(xor(exp,xor(km,xor(kp,kp)))))]]) ).
cnf(refute_0_87,plain,
( xor(km,xor(exp,xor(kp,kp))) != xor(exp,xor(km,xor(kp,kp)))
| xor(km,xor(kp,xor(exp,kp))) = xor(exp,xor(km,xor(kp,kp))) ),
inference(resolve,[$cnf( $equal(xor(km,xor(kp,xor(exp,kp))),xor(km,xor(exp,xor(kp,kp)))) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
xor(km,xor(kp,xor(exp,kp))) = xor(exp,xor(km,xor(kp,kp))),
inference(resolve,[$cnf( $equal(xor(km,xor(exp,xor(kp,kp))),xor(exp,xor(km,xor(kp,kp)))) )],[refute_0_84,refute_0_87]) ).
cnf(refute_0_89,plain,
( xor(exp,xor(km,xor(kp,kp))) != xor(exp,km)
| xor(km,xor(kp,xor(exp,kp))) != xor(exp,xor(km,xor(kp,kp)))
| xor(km,xor(kp,xor(exp,kp))) = xor(exp,km) ),
inference(subst,[],[refute_0_35:[bind(X0,$fot(xor(km,xor(kp,xor(exp,kp))))),bind(Y,$fot(xor(exp,xor(km,xor(kp,kp))))),bind(Z,$fot(xor(exp,km)))]]) ).
cnf(refute_0_90,plain,
( xor(exp,xor(km,xor(kp,kp))) != xor(exp,km)
| xor(km,xor(kp,xor(exp,kp))) = xor(exp,km) ),
inference(resolve,[$cnf( $equal(xor(km,xor(kp,xor(exp,kp))),xor(exp,xor(km,xor(kp,kp)))) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
xor(km,xor(kp,xor(exp,kp))) = xor(exp,km),
inference(resolve,[$cnf( $equal(xor(exp,xor(km,xor(kp,kp))),xor(exp,km)) )],[refute_0_42,refute_0_90]) ).
cnf(refute_0_92,plain,
crypt(xor(km,xor(kp,xor(exp,kp))),xor(exp,kp)) = crypt(xor(km,xor(kp,xor(exp,kp))),xor(exp,kp)),
introduced(tautology,[refl,[$fot(crypt(xor(km,xor(kp,xor(exp,kp))),xor(exp,kp)))]]) ).
cnf(refute_0_93,plain,
( crypt(xor(km,xor(kp,xor(exp,kp))),xor(exp,kp)) != crypt(xor(km,xor(kp,xor(exp,kp))),xor(exp,kp))
| xor(km,xor(kp,xor(exp,kp))) != xor(exp,km)
| crypt(xor(km,xor(kp,xor(exp,kp))),xor(exp,kp)) = crypt(xor(exp,km),xor(exp,kp)) ),
introduced(tautology,[equality,[$cnf( $equal(crypt(xor(km,xor(kp,xor(exp,kp))),xor(exp,kp)),crypt(xor(km,xor(kp,xor(exp,kp))),xor(exp,kp))) ),[1,0],$fot(xor(exp,km))]]) ).
cnf(refute_0_94,plain,
( xor(km,xor(kp,xor(exp,kp))) != xor(exp,km)
| crypt(xor(km,xor(kp,xor(exp,kp))),xor(exp,kp)) = crypt(xor(exp,km),xor(exp,kp)) ),
inference(resolve,[$cnf( $equal(crypt(xor(km,xor(kp,xor(exp,kp))),xor(exp,kp)),crypt(xor(km,xor(kp,xor(exp,kp))),xor(exp,kp))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
crypt(xor(km,xor(kp,xor(exp,kp))),xor(exp,kp)) = crypt(xor(exp,km),xor(exp,kp)),
inference(resolve,[$cnf( $equal(xor(km,xor(kp,xor(exp,kp))),xor(exp,km)) )],[refute_0_91,refute_0_94]) ).
cnf(refute_0_96,plain,
( crypt(xor(km,xor(kp,xor(exp,kp))),xor(exp,kp)) != crypt(xor(exp,km),xor(exp,kp))
| ~ p(crypt(xor(km,xor(kp,xor(exp,kp))),xor(exp,kp)))
| p(crypt(xor(exp,km),xor(exp,kp))) ),
introduced(tautology,[equality,[$cnf( p(crypt(xor(km,xor(kp,xor(exp,kp))),xor(exp,kp))) ),[0],$fot(crypt(xor(exp,km),xor(exp,kp)))]]) ).
cnf(refute_0_97,plain,
( ~ p(crypt(xor(km,xor(kp,xor(exp,kp))),xor(exp,kp)))
| p(crypt(xor(exp,km),xor(exp,kp))) ),
inference(resolve,[$cnf( $equal(crypt(xor(km,xor(kp,xor(exp,kp))),xor(exp,kp)),crypt(xor(exp,km),xor(exp,kp))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
p(crypt(xor(exp,km),xor(exp,kp))),
inference(resolve,[$cnf( p(crypt(xor(km,xor(kp,xor(exp,kp))),xor(exp,kp))) )],[refute_0_25,refute_0_97]) ).
cnf(refute_0_99,plain,
~ p(xor(exp,kp)),
inference(resolve,[$cnf( p(crypt(xor(exp,km),xor(exp,kp))) )],[refute_0_98,refute_0_15]) ).
cnf(refute_0_100,plain,
$false,
inference(resolve,[$cnf( p(xor(exp,kp)) )],[refute_0_24,refute_0_99]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWV236+1 : TPTP v8.1.0. Released v3.2.0.
% 0.10/0.12 % Command : metis --show proof --show saturation %s
% 0.14/0.34 % Computer : n023.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Tue Jun 14 22:40:20 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.56/2.72 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.56/2.72
% 2.56/2.72 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.56/2.73
%------------------------------------------------------------------------------