%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV235+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n003.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 : 300s
% DateTime : Tue May 5 05:21:08 PM UTC 2026
% Result : Theorem 1.51s 1.79s
% Output : CNFRefutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 16
% Syntax : Number of formulae : 58 ( 31 unt; 0 def)
% Number of atoms : 112 ( 15 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 97 ( 43 ~; 40 |; 8 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 7 con; 0-2 aty)
% Number of variables : 82 ( 1 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(key_part_import___part_2,axiom,
! [X6,X9,X11] :
( ( p(X6)
& p(crypt(xor(km,xor(kp,X9)),X11))
& p(X9) )
=> p(crypt(xor(km,xor(X9,kp)),xor(X6,X11))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_part_import___part_2) ).
fof(xor_rules_2,axiom,
! [X1] : xor(X1,X1) = id,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_rules_2) ).
fof(key_part_import___part_1,axiom,
! [X10,X9] :
( ( p(X10)
& p(X9) )
=> p(crypt(xor(km,xor(kp,X9)),X10)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_part_import___part_1) ).
fof(xor_rules_1,axiom,
! [X1] : xor(X1,id) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_rules_1) ).
fof(xor_commutative,axiom,
! [X1,X2] : xor(X1,X2) = xor(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutative) ).
fof(an_account_number,axiom,
p(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_account_number) ).
fof(xor_associative,axiom,
! [X1,X2,X3] : xor(X1,xor(X2,X3)) = xor(xor(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_associative) ).
fof(combine_with_XOR,axiom,
! [X1,X2] :
( ( p(X1)
& p(X2) )
=> p(xor(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',combine_with_XOR) ).
fof(key_export,axiom,
! [X9,X6,X4] :
( ( p(crypt(xor(km,X9),X6))
& p(X9)
& p(crypt(xor(km,exp),X4)) )
=> p(crypt(xor(X4,X9),X6)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_export) ).
fof(initial_knowledge_of_intruder_1,axiom,
p(kp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_1) ).
fof(initial_knowledge_of_intruder_11,axiom,
p(exp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_11) ).
fof(find_pin,conjecture,
p(crypt(pp,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',find_pin) ).
fof(encrypt_knowledge,axiom,
! [X1,X2] :
( ( p(X2)
& p(X1) )
=> p(crypt(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_knowledge) ).
fof(decrypt_knowledge,axiom,
! [X1,X2] :
( ( p(crypt(X1,X2))
& p(X1) )
=> p(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',decrypt_knowledge) ).
fof(initial_knowledge_of_intruder_6,axiom,
p(crypt(xor(km,pin),pp)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_6) ).
fof(initial_knowledge_of_intruder_5,axiom,
p(pin),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge_of_intruder_5) ).
fof(c_0_16,plain,
! [X72,X73,X74] :
( ~ p(X72)
| ~ p(crypt(xor(km,xor(kp,X73)),X74))
| ~ p(X73)
| p(crypt(xor(km,xor(X73,kp)),xor(X72,X74))) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[key_part_import___part_2])]) ).
fof(c_0_17,plain,
! [X61] : xor(X61,X61) = id,
inference(variable_rename,[status(thm)],[xor_rules_2]) ).
fof(c_0_18,plain,
! [X70,X71] :
( ~ p(X70)
| ~ p(X71)
| p(crypt(xor(km,xor(kp,X71)),X70)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[key_part_import___part_1])]) ).
cnf(c_0_19,plain,
( p(crypt(xor(km,xor(X2,kp)),xor(X1,X3)))
| ~ p(X1)
| ~ p(crypt(xor(km,xor(kp,X2)),X3))
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
xor(X1,X1) = id,
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
( p(crypt(xor(km,xor(kp,X2)),X1))
| ~ p(X1)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
fof(c_0_22,plain,
! [X60] : xor(X60,id) = X60,
inference(variable_rename,[status(thm)],[xor_rules_1]) ).
fof(c_0_23,plain,
! [X53,X54] : xor(X53,X54) = xor(X54,X53),
inference(variable_rename,[status(thm)],[xor_commutative]) ).
cnf(c_0_24,plain,
( p(crypt(xor(km,xor(X1,kp)),id))
| ~ p(X1)
| ~ p(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
cnf(c_0_25,plain,
p(a),
inference(split_conjunct,[status(thm)],[an_account_number]) ).
fof(c_0_26,plain,
! [X55,X56,X57] : xor(X55,xor(X56,X57)) = xor(xor(X55,X56),X57),
inference(variable_rename,[status(thm)],[xor_associative]) ).
cnf(c_0_27,plain,
xor(X1,id) = X1,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
xor(X1,X2) = xor(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
( p(crypt(xor(km,xor(X1,kp)),id))
| ~ p(X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
xor(X1,xor(X2,X3)) = xor(xor(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_31,plain,
xor(id,X1) = X1,
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,plain,
( p(crypt(xor(km,xor(kp,X1)),id))
| ~ p(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_33,plain,
xor(X1,xor(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_20]),c_0_31]) ).
cnf(c_0_34,plain,
( p(crypt(xor(km,X1),id))
| ~ p(xor(kp,X1)) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_35,plain,
xor(X1,xor(X2,X3)) = xor(X2,xor(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_28]),c_0_30]) ).
fof(c_0_36,plain,
! [X88,X89] :
( ~ p(X88)
| ~ p(X89)
| p(xor(X88,X89)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[combine_with_XOR])]) ).
cnf(c_0_37,plain,
( p(crypt(X1,id))
| ~ p(xor(km,xor(kp,X1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_33]),c_0_35]) ).
cnf(c_0_38,plain,
( p(xor(X1,X2))
| ~ p(X1)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_36]) ).
fof(c_0_39,plain,
! [X67,X68,X69] :
( ~ p(crypt(xor(km,X67),X68))
| ~ p(X67)
| ~ p(crypt(xor(km,exp),X69))
| p(crypt(xor(X69,X67),X68)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[key_export])]) ).
cnf(c_0_40,plain,
( p(crypt(X1,id))
| ~ p(xor(km,xor(X1,kp))) ),
inference(spm,[status(thm)],[c_0_37,c_0_28]) ).
cnf(c_0_41,plain,
( p(xor(X1,xor(X2,X3)))
| ~ p(xor(X1,X2))
| ~ p(X3) ),
inference(spm,[status(thm)],[c_0_38,c_0_30]) ).
cnf(c_0_42,plain,
p(kp),
inference(split_conjunct,[status(thm)],[initial_knowledge_of_intruder_1]) ).
cnf(c_0_43,plain,
( p(crypt(xor(X3,X1),X2))
| ~ p(crypt(xor(km,X1),X2))
| ~ p(X1)
| ~ p(crypt(xor(km,exp),X3)) ),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_44,plain,
( p(crypt(X1,id))
| ~ p(xor(km,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_42])]) ).
cnf(c_0_45,plain,
p(exp),
inference(split_conjunct,[status(thm)],[initial_knowledge_of_intruder_11]) ).
fof(c_0_46,negated_conjecture,
~ p(crypt(pp,a)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[find_pin])]) ).
fof(c_0_47,plain,
! [X92,X93] :
( ~ p(X93)
| ~ p(X92)
| p(crypt(X92,X93)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[encrypt_knowledge])]) ).
fof(c_0_48,plain,
! [X90,X91] :
( ~ p(crypt(X90,X91))
| ~ p(X90)
| p(X91) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[decrypt_knowledge])]) ).
cnf(c_0_49,plain,
( p(crypt(X1,X2))
| ~ p(crypt(xor(km,X1),X2))
| ~ p(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_31]),c_0_33]),c_0_45])]) ).
cnf(c_0_50,plain,
p(crypt(xor(km,pin),pp)),
inference(split_conjunct,[status(thm)],[initial_knowledge_of_intruder_6]) ).
cnf(c_0_51,plain,
p(pin),
inference(split_conjunct,[status(thm)],[initial_knowledge_of_intruder_5]) ).
cnf(c_0_52,negated_conjecture,
~ p(crypt(pp,a)),
inference(split_conjunct,[status(thm)],[c_0_46]) ).
cnf(c_0_53,plain,
( p(crypt(X2,X1))
| ~ p(X1)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_54,plain,
( p(X2)
| ~ p(crypt(X1,X2))
| ~ p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_48]) ).
cnf(c_0_55,plain,
p(crypt(pin,pp)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_51])]) ).
cnf(c_0_56,negated_conjecture,
~ p(pp),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_25])]) ).
cnf(c_0_57,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_51])]),c_0_56]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV235+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n003.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:58:11 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.51/1.79 % Version : CSE_E---1.7
% 1.51/1.79 % Problem : theBenchmark.p
% 1.51/1.79 % SZS status Theorem for theBenchmark.p
% 1.51/1.79 % SZS output start CNFRefutation
% See solution above
% 1.51/1.79 % Total time : 1.368s
%------------------------------------------------------------------------------