%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV235+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n004.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 : Sun Sep 27 09:07:05 AM UTC 2026
% Result : Theorem 13.93s 2.43s
% Output : CNFRefutation 13.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 16
% Syntax : Number of formulae : 53 ( 36 unt; 0 def)
% Number of atoms : 83 ( 13 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 54 ( 24 ~; 19 |; 6 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(xor_commutative,axiom,
! [X1,X2] : xor(X1,X2) = xor(X2,X1),
file('theBenchmark.p',xor_commutative) ).
fof(xor_associative,axiom,
! [X1,X2,X3] : xor(X1,xor(X2,X3)) = xor(xor(X1,X2),X3),
file('theBenchmark.p',xor_associative) ).
fof(xor_rules_1,axiom,
! [X1] : xor(X1,id) = X1,
file('theBenchmark.p',xor_rules_1) ).
fof(xor_rules_2,axiom,
! [X1] : xor(X1,X1) = id,
file('theBenchmark.p',xor_rules_2) ).
fof(key_export,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('theBenchmark.p',key_export) ).
fof(key_part_import___part_1,axiom,
! [Xk,Xtype] :
( ( p(Xtype)
& p(Xk) )
=> p(crypt(xor(km,xor(kp,Xtype)),Xk)) ),
file('theBenchmark.p',key_part_import___part_1) ).
fof(combine_with_XOR,axiom,
! [X1,X2] :
( ( p(X2)
& p(X1) )
=> p(xor(X1,X2)) ),
file('theBenchmark.p',combine_with_XOR) ).
fof(decrypt_knowledge,axiom,
! [X1,X2] :
( ( p(X1)
& p(crypt(X1,X2)) )
=> p(X2) ),
file('theBenchmark.p',decrypt_knowledge) ).
fof(encrypt_knowledge,axiom,
! [X1,X2] :
( ( p(X1)
& p(X2) )
=> p(crypt(X1,X2)) ),
file('theBenchmark.p',encrypt_knowledge) ).
fof(find_pin,conjecture,
p(crypt(pp,a)),
file('theBenchmark.p',find_pin) ).
fof(find_pin_neg,negated_conjecture,
~ p(crypt(pp,a)),
inference(assume_negation,[status(cth)],[find_pin]) ).
cnf(c_18,plain,
xor(A,B) = xor(B,A),
inference(clausify,[status(thm)],[xor_commutative]) ).
cnf(c_19,plain,
xor(xor(A,B),C) = xor(A,xor(B,C)),
inference(clausify,[status(thm)],[xor_associative]) ).
cnf(c_21,plain,
xor(A,id) = A,
inference(clausify,[status(thm)],[xor_rules_1]) ).
cnf(c_22,plain,
xor(A,A) = id,
inference(clausify,[status(thm)],[xor_rules_2]) ).
cnf(c_24,plain,
( p(crypt(xor(C,A),B))
| ~ p(crypt(xor(km,exp),C))
| ~ p(A)
| ~ p(crypt(xor(km,A),B)) ),
inference(clausify,[status(thm)],[key_export]) ).
cnf(c_25,plain,
( p(crypt(xor(km,xor(kp,B)),A))
| ~ p(B)
| ~ p(A) ),
inference(clausify,[status(thm)],[key_part_import___part_1]) ).
cnf(c_31,plain,
( p(xor(A,B))
| ~ p(B)
| ~ p(A) ),
inference(clausify,[status(thm)],[combine_with_XOR]) ).
cnf(c_32,plain,
( p(B)
| ~ p(A)
| ~ p(crypt(A,B)) ),
inference(clausify,[status(thm)],[decrypt_knowledge]) ).
cnf(c_33,plain,
( p(crypt(B,A))
| ~ p(B)
| ~ p(A) ),
inference(clausify,[status(thm)],[encrypt_knowledge]) ).
fof(initial_knowledge_of_intruder_1,axiom,
p(kp),
file('theBenchmark.p',initial_knowledge_of_intruder_1) ).
cnf(c_34,plain,
p(kp),
inference(clausify,[status(thm)],[initial_knowledge_of_intruder_1]) ).
fof(initial_knowledge_of_intruder_3,axiom,
p(data),
file('theBenchmark.p',initial_knowledge_of_intruder_3) ).
cnf(c_36,plain,
p(data),
inference(clausify,[status(thm)],[initial_knowledge_of_intruder_3]) ).
fof(initial_knowledge_of_intruder_5,axiom,
p(pin),
file('theBenchmark.p',initial_knowledge_of_intruder_5) ).
cnf(c_38,plain,
p(pin),
inference(clausify,[status(thm)],[initial_knowledge_of_intruder_5]) ).
fof(initial_knowledge_of_intruder_6,axiom,
p(crypt(xor(km,pin),pp)),
file('theBenchmark.p',initial_knowledge_of_intruder_6) ).
cnf(c_39,plain,
p(crypt(xor(km,pin),pp)),
inference(clausify,[status(thm)],[initial_knowledge_of_intruder_6]) ).
fof(initial_knowledge_of_intruder_11,axiom,
p(exp),
file('theBenchmark.p',initial_knowledge_of_intruder_11) ).
cnf(c_45,plain,
p(exp),
inference(clausify,[status(thm)],[initial_knowledge_of_intruder_11]) ).
fof(an_account_number,axiom,
p(a),
file('theBenchmark.p',an_account_number) ).
cnf(c_46,plain,
p(a),
inference(clausify,[status(thm)],[an_account_number]) ).
cnf(c_47,negated_conjecture,
~ p(crypt(pp,a)),
inference(clausify,[status(thm)],[find_pin_neg]) ).
cnf(c_13448,plain,
A = xor(id,A),
inference(paramod,[status(thm)],[c_21,c_18]) ).
cnf(c_74,plain,
xor(id,A) = A,
inference(copy,[status(thm)],[c_13448]) ).
cnf(c_13449,plain,
xor(id,A) = xor(B,xor(B,A)),
inference(paramod,[status(thm)],[c_22,c_19]) ).
cnf(c_13450,plain,
A = xor(B,xor(B,A)),
inference(paramod,[status(thm)],[c_74,c_13449]) ).
cnf(c_75,plain,
xor(A,xor(A,B)) = B,
inference(copy,[status(thm)],[c_13450]) ).
cnf(c_13451,plain,
( p(xor(data,A))
| ~ p(A) ),
inference(resolve,[status(thm)],[c_31,c_36]) ).
cnf(c_122,plain,
p(xor(data,pin)),
inference(resolve,[status(thm)],[c_13451,c_38]) ).
cnf(c_13452,plain,
( p(xor(kp,A))
| ~ p(A) ),
inference(resolve,[status(thm)],[c_31,c_34]) ).
cnf(c_338,plain,
p(xor(kp,exp)),
inference(resolve,[status(thm)],[c_13452,c_45]) ).
cnf(c_13453,plain,
( p(crypt(A,a))
| ~ p(A) ),
inference(resolve,[status(thm)],[c_33,c_46]) ).
cnf(c_419,negated_conjecture,
~ p(pp),
inference(resolve,[status(thm)],[c_13453,c_47]) ).
cnf(c_13454,plain,
( p(A)
| ~ p(crypt(xor(data,pin),A)) ),
inference(resolve,[status(thm)],[c_32,c_122]) ).
cnf(c_7076,plain,
~ p(crypt(xor(data,pin),pp)),
inference(resolve,[status(thm)],[c_13454,c_419]) ).
cnf(c_13455,plain,
( p(crypt(xor(A,pin),pp))
| ~ p(crypt(xor(km,exp),A))
| ~ p(pin) ),
inference(resolve,[status(thm)],[c_24,c_39]) ).
cnf(c_13456,plain,
( p(crypt(xor(A,pin),pp))
| ~ p(crypt(xor(km,exp),A)) ),
inference(resolve,[status(thm)],[c_13455,c_38]) ).
cnf(c_12506,plain,
~ p(crypt(xor(km,exp),data)),
inference(resolve,[status(thm)],[c_13456,c_7076]) ).
cnf(c_13457,plain,
( p(crypt(xor(km,xor(kp,A)),data))
| ~ p(A) ),
inference(resolve,[status(thm)],[c_25,c_36]) ).
cnf(c_13458,plain,
p(crypt(xor(km,xor(kp,xor(kp,exp))),data)),
inference(resolve,[status(thm)],[c_13457,c_338]) ).
cnf(c_13459,plain,
p(crypt(xor(km,exp),data)),
inference(paramod,[status(thm)],[c_75,c_13458]) ).
cnf(c_13447,plain,
$false,
inference(resolve,[status(thm)],[c_12506,c_13459]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV235+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n004.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 : Sat Sep 26 13:21:07 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1809408 was started by sandbox2 on n004,
% 0.08/0.36 % Sat Sep 26 13:21:07 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 13.93/2.43
% 13.93/2.43 % SZS status Theorem for theBenchmark
% 13.93/2.43
% 13.93/2.43 % Proof 1 at 1.65 (+ 0.33) seconds.
% 13.93/2.43 % Length of proof is 34.
% 13.93/2.43 % Level of proof is 5.
% 13.93/2.43 % Maximum clause weight is 35.000.
% 13.93/2.43 % Given clauses 147.
% 13.93/2.43
% 13.93/2.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------