%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SWV235+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 : Fri Sep 25 03:12:33 PM UTC 2026
% Result : Theorem 6.68s 1.37s
% Output : Proof 6.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 13
% Syntax : Number of formulae : 77 ( 49 unt; 0 def)
% Number of atoms : 145 ( 28 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 125 ( 57 ~; 51 |; 10 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-4 aty)
% Number of variables : 85 ( 0 sgn 51 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f20,axiom,
p(pin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_5) ).
fof(f20_nnf,plain,
p(pin),
inference(nnf_transformation,[status(thm)],[f20]) ).
cnf(c20,plain,
p(pin),
inference(cnf_transformation,[status(esa)],[f20_nnf]) ).
cnf(hi20,axiom,
p(pin) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(h1,plain,
p(pin) = true,
inference(hyper_resolution,[status(thm)],[hi20]) ).
fof(f13,axiom,
! [X1,X2] :
( ( p(X2)
& p(X1) )
=> p(xor(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',combine_with_XOR) ).
fof(f13_nnf,plain,
! [X1,X2] :
( p(xor(X1,X2))
| ~ p(X2)
| ~ p(X1) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X1,X2] :
( p(xor(X1,X2))
| ~ p(X2)
| ~ p(X1) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( p(xor(X0,X1))
| ~ p(X1)
| ~ p(X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi13,axiom,
ifeq(p(X0),true,ifeq(p(X1),true,p(xor(X0,X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
fof(f16,axiom,
p(kp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_1) ).
fof(f16_nnf,plain,
p(kp),
inference(nnf_transformation,[status(thm)],[f16]) ).
cnf(c16,plain,
p(kp),
inference(cnf_transformation,[status(esa)],[f16_nnf]) ).
cnf(hi16,axiom,
p(kp) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h12,plain,
p(xor(kp,kp)) = true,
inference(hyper_resolution,[status(thm)],[hi13,hi16,hi16]) ).
cnf(h13,plain,
p(xor(xor(kp,kp),kp)) = true,
inference(hyper_resolution,[status(thm)],[hi13,h12,hi16]) ).
cnf(h14,plain,
p(xor(xor(xor(kp,kp),kp),pin)) = true,
inference(hyper_resolution,[status(thm)],[hi13,h13,h1]) ).
fof(f26,axiom,
p(exp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_11) ).
fof(f26_nnf,plain,
p(exp),
inference(nnf_transformation,[status(thm)],[f26]) ).
cnf(c26,plain,
p(exp),
inference(cnf_transformation,[status(esa)],[f26_nnf]) ).
cnf(hi26,axiom,
p(exp) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(h2,plain,
p(exp) = true,
inference(hyper_resolution,[status(thm)],[hi26]) ).
cnf(h4,plain,
p(kp) = true,
inference(hyper_resolution,[status(thm)],[hi16]) ).
fof(f7,axiom,
! [Xk,Xtype] :
( ( p(Xtype)
& p(Xk) )
=> p(crypt(xor(km,xor(kp,Xtype)),Xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',key_part_import___part_1) ).
fof(f7_nnf,plain,
! [Xk,Xtype] :
( p(crypt(xor(km,xor(kp,Xtype)),Xk))
| ~ p(Xtype)
| ~ p(Xk) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [Xk,Xtype] :
( p(crypt(xor(km,xor(kp,Xtype)),Xk))
| ~ p(Xtype)
| ~ p(Xk) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( p(crypt(xor(km,xor(kp,X1)),X0))
| ~ p(X1)
| ~ p(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(p(X0),true,ifeq(p(X1),true,p(crypt(xor(km,xor(kp,X1)),X0)),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h8,plain,
p(crypt(xor(km,xor(kp,exp)),kp)) = true,
inference(hyper_resolution,[status(thm)],[hi7,h4,h2]) ).
fof(f8,axiom,
! [Xk1,Xtype,Xk2] :
( ( p(Xtype)
& p(crypt(xor(km,xor(kp,Xtype)),Xk2))
& p(Xk1) )
=> p(crypt(xor(km,xor(Xtype,kp)),xor(Xk1,Xk2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',key_part_import___part_2) ).
fof(f8_nnf,plain,
! [Xk1,Xtype,Xk2] :
( p(crypt(xor(km,xor(Xtype,kp)),xor(Xk1,Xk2)))
| ~ p(Xtype)
| ~ p(crypt(xor(km,xor(kp,Xtype)),Xk2))
| ~ p(Xk1) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [Xk1,Xtype,Xk2] :
( p(crypt(xor(km,xor(Xtype,kp)),xor(Xk1,Xk2)))
| ~ p(Xtype)
| ~ p(crypt(xor(km,xor(kp,Xtype)),Xk2))
| ~ p(Xk1) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( p(crypt(xor(km,xor(X1,kp)),xor(X0,X2)))
| ~ p(X1)
| ~ p(crypt(xor(km,xor(kp,X1)),X2))
| ~ p(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,axiom,
ifeq(p(X0),true,ifeq(p(crypt(xor(km,xor(kp,X1)),X2)),true,ifeq(p(X1),true,p(crypt(xor(km,xor(X1,kp)),xor(X0,X2))),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h9,plain,
p(crypt(xor(km,xor(exp,kp)),xor(kp,kp))) = true,
inference(hyper_resolution,[status(thm)],[hi8,h4,h8,h2]) ).
fof(f9,axiom,
! [Xk1,Xtype,Xk2] :
( ( p(Xtype)
& p(crypt(xor(km,xor(Xtype,kp)),Xk2))
& p(Xk1) )
=> p(crypt(xor(km,Xtype),xor(Xk2,Xk1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',key_part_import___part_3) ).
fof(f9_nnf,plain,
! [Xk1,Xtype,Xk2] :
( p(crypt(xor(km,Xtype),xor(Xk2,Xk1)))
| ~ p(Xtype)
| ~ p(crypt(xor(km,xor(Xtype,kp)),Xk2))
| ~ p(Xk1) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [Xk1,Xtype,Xk2] :
( p(crypt(xor(km,Xtype),xor(Xk2,Xk1)))
| ~ p(Xtype)
| ~ p(crypt(xor(km,xor(Xtype,kp)),Xk2))
| ~ p(Xk1) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( p(crypt(xor(km,X1),xor(X2,X0)))
| ~ p(X1)
| ~ p(crypt(xor(km,xor(X1,kp)),X2))
| ~ p(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,axiom,
ifeq(p(X0),true,ifeq(p(crypt(xor(km,xor(X1,kp)),X2)),true,ifeq(p(X1),true,p(crypt(xor(km,X1),xor(X2,X0))),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h10,plain,
p(crypt(xor(km,exp),xor(xor(kp,kp),kp))) = true,
inference(hyper_resolution,[status(thm)],[hi9,h4,h9,h2]) ).
fof(f6,axiom,
! [Xtype,Xk1,Xkek1] :
( ( p(crypt(xor(km,exp),Xkek1))
& p(Xtype)
& p(crypt(xor(km,Xtype),Xk1)) )
=> p(crypt(xor(Xkek1,Xtype),Xk1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',key_export) ).
fof(f6_nnf,plain,
! [Xtype,Xk1,Xkek1] :
( p(crypt(xor(Xkek1,Xtype),Xk1))
| ~ p(crypt(xor(km,exp),Xkek1))
| ~ p(Xtype)
| ~ p(crypt(xor(km,Xtype),Xk1)) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [Xtype,Xk1,Xkek1] :
( p(crypt(xor(Xkek1,Xtype),Xk1))
| ~ p(crypt(xor(km,exp),Xkek1))
| ~ p(Xtype)
| ~ p(crypt(xor(km,Xtype),Xk1)) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( p(crypt(xor(X2,X0),X1))
| ~ p(crypt(xor(km,exp),X2))
| ~ p(X0)
| ~ p(crypt(xor(km,X0),X1)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(p(crypt(xor(km,X0),X1)),true,ifeq(p(X0),true,ifeq(p(crypt(xor(km,exp),X2)),true,p(crypt(xor(X2,X0),X1)),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
fof(f21,axiom,
p(crypt(xor(km,pin),pp)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_knowledge_of_intruder_6) ).
fof(f21_nnf,plain,
p(crypt(xor(km,pin),pp)),
inference(nnf_transformation,[status(thm)],[f21]) ).
cnf(c21,plain,
p(crypt(xor(km,pin),pp)),
inference(cnf_transformation,[status(esa)],[f21_nnf]) ).
cnf(hi21,axiom,
p(crypt(xor(km,pin),pp)) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(h11,plain,
p(crypt(xor(xor(xor(kp,kp),kp),pin),pp)) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi21,h1,h10]) ).
fof(f14,axiom,
! [X1,X2] :
( ( p(X1)
& p(crypt(X1,X2)) )
=> p(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',decrypt_knowledge) ).
fof(f14_nnf,plain,
! [X1,X2] :
( p(X2)
| ~ p(X1)
| ~ p(crypt(X1,X2)) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X1,X2] :
( p(X2)
| ~ p(X1)
| ~ p(crypt(X1,X2)) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( p(X1)
| ~ p(X0)
| ~ p(crypt(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,axiom,
ifeq(p(crypt(X0,X1)),true,ifeq(p(X0),true,p(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h15,plain,
p(pp) = true,
inference(hyper_resolution,[status(thm)],[hi14,h11,h14]) ).
fof(f27,axiom,
p(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',an_account_number) ).
fof(f27_nnf,plain,
p(a),
inference(nnf_transformation,[status(thm)],[f27]) ).
cnf(c27,plain,
p(a),
inference(cnf_transformation,[status(esa)],[f27_nnf]) ).
cnf(hi27,axiom,
p(a) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(h0,plain,
p(a) = true,
inference(hyper_resolution,[status(thm)],[hi27]) ).
fof(f15,axiom,
! [X1,X2] :
( ( p(X1)
& p(X2) )
=> p(crypt(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',encrypt_knowledge) ).
fof(f15_nnf,plain,
! [X1,X2] :
( p(crypt(X1,X2))
| ~ p(X1)
| ~ p(X2) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X2,X1] :
( p(crypt(X1,X2))
| ~ p(X1)
| ~ p(X2) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( p(crypt(X0,X1))
| ~ p(X0)
| ~ p(X1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi15,axiom,
ifeq(p(X0),true,ifeq(p(X1),true,p(crypt(X1,X0)),true),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t9,plain,
p(crypt(pp,a)) = true,
inference(hyper_resolution,[status(thm)],[hi15,h0,h15]) ).
cnf(t38,plain,
p(crypt(pp,a)) = true,
inference(orient,[status(thm)],[t9]) ).
fof(f28,conjecture,
p(crypt(pp,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',find_pin) ).
fof(f28_neg,negated_conjecture,
~ p(crypt(pp,a)),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f28_nnf,plain,
~ p(crypt(pp,a)),
inference(nnf_transformation,[status(thm)],[f28_neg]) ).
fof(f28_sk,plain,
~ p(crypt(pp,a)),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
~ p(crypt(pp,a)),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(goal_0,negated_conjecture,
p(crypt(pp,a)) != true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t38]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV235+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n013.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 18:48:21 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.68/1.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.68/1.37 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------