%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV234+2 : 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 : n019.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 1.41s 1.80s
% Output : CNFRefutation 1.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 12
% Syntax : Number of formulae : 48 ( 37 unt; 0 def)
% Number of atoms : 71 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 43 ( 20 ~; 18 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 69 ( 6 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(xor_zero,axiom,
! [X1,X2,X3] : xor(X1,z) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_zero) ).
fof(xor_commutes,axiom,
! [X1,X2,X3] : xor(X1,X2) = xor(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutes) ).
fof(xor_assosciative,axiom,
! [X1,X2,X3] : xor(X1,xor(X2,X3)) = xor(xor(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_assosciative) ).
fof(xor_self_cancel,axiom,
! [X1,X2,X3] : xor(X1,X1) = z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_self_cancel) ).
fof(initial_knowledge9,axiom,
public(enc(xor(km,imp),xor(kek,xor(pin,data)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge9) ).
fof(key_import_cmd,axiom,
! [X1,X2,X3] :
( ( public(X2)
& public(enc(xor(X1,X2),X3))
& public(enc(xor(km,imp),X1)) )
=> public(enc(xor(km,X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_import_cmd) ).
fof(encrypt_data_cmd,axiom,
! [X1,X2] :
( ( public(X1)
& public(X2) )
=> public(enc(enc(inv(xor(data,km)),X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_data_cmd) ).
fof(encrypt_decrypt_cancel,axiom,
! [X1,X2,X3] : enc(X1,enc(inv(X1),X2)) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_decrypt_cancel) ).
fof(initial_knowledge2,axiom,
public(data),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge2) ).
fof(initial_knowledge5,axiom,
public(enc(xor(kek,pin),pp)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge5) ).
fof(co1,conjecture,
public(enc(pp,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(initial_knowledge8,axiom,
public(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge8) ).
fof(c_0_12,plain,
! [X57] : xor(X57,z) = X57,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[xor_zero])]) ).
fof(c_0_13,plain,
! [X51,X52] : xor(X51,X52) = xor(X52,X51),
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[xor_commutes])]) ).
fof(c_0_14,plain,
! [X53,X54,X55] : xor(X53,xor(X54,X55)) = xor(xor(X53,X54),X55),
inference(variable_rename,[status(thm)],[xor_assosciative]) ).
fof(c_0_15,plain,
! [X56] : xor(X56,X56) = z,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[xor_self_cancel])]) ).
cnf(c_0_16,plain,
xor(X1,z) = X1,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
xor(X1,X2) = xor(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,plain,
public(enc(xor(km,imp),xor(kek,xor(pin,data)))),
inference(split_conjunct,[status(thm)],[initial_knowledge9]) ).
cnf(c_0_19,plain,
xor(X1,xor(X2,X3)) = xor(xor(X1,X2),X3),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
xor(X1,X1) = z,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
xor(z,X1) = X1,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
fof(c_0_22,plain,
! [X43,X44,X45] :
( ~ public(X44)
| ~ public(enc(xor(X43,X44),X45))
| ~ public(enc(xor(km,imp),X43))
| public(enc(xor(km,X44),X45)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[key_import_cmd])]) ).
cnf(c_0_23,plain,
public(enc(xor(km,imp),xor(kek,xor(data,pin)))),
inference(rw,[status(thm)],[c_0_18,c_0_17]) ).
cnf(c_0_24,plain,
xor(X1,xor(X2,X3)) = xor(X2,xor(X3,X1)),
inference(spm,[status(thm)],[c_0_19,c_0_17]) ).
cnf(c_0_25,plain,
xor(X1,xor(X1,X2)) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).
fof(c_0_26,plain,
! [X41,X42] :
( ~ public(X41)
| ~ public(X42)
| public(enc(enc(inv(xor(data,km)),X41),X42)) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[encrypt_data_cmd])]) ).
fof(c_0_27,plain,
! [X49,X50] : enc(X49,enc(inv(X49),X50)) = X50,
inference(variable_rename,[status(thm)],[inference(fof_simplification,[status(thm)],[encrypt_decrypt_cancel])]) ).
cnf(c_0_28,plain,
( public(enc(xor(km,X1),X3))
| ~ public(X1)
| ~ public(enc(xor(X2,X1),X3))
| ~ public(enc(xor(km,imp),X2)) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,plain,
public(enc(xor(km,imp),xor(data,xor(pin,kek)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_17]),c_0_24]),c_0_17]) ).
cnf(c_0_30,plain,
xor(X1,xor(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_25,c_0_17]) ).
cnf(c_0_31,plain,
( public(enc(enc(inv(xor(data,km)),X1),X2))
| ~ public(X1)
| ~ public(X2) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
cnf(c_0_32,plain,
enc(X1,enc(inv(X1),X2)) = X2,
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_33,plain,
( public(enc(xor(km,X1),X2))
| ~ public(enc(xor(data,xor(pin,xor(kek,X1))),X2))
| ~ public(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_19]),c_0_19]) ).
cnf(c_0_34,plain,
xor(X1,xor(X2,xor(X3,X1))) = xor(X2,X3),
inference(spm,[status(thm)],[c_0_30,c_0_19]) ).
cnf(c_0_35,plain,
public(data),
inference(split_conjunct,[status(thm)],[initial_knowledge2]) ).
cnf(c_0_36,plain,
public(enc(xor(kek,pin),pp)),
inference(split_conjunct,[status(thm)],[initial_knowledge5]) ).
cnf(c_0_37,plain,
( public(enc(enc(inv(xor(km,data)),X1),X2))
| ~ public(X2)
| ~ public(X1) ),
inference(rw,[status(thm)],[c_0_31,c_0_17]) ).
cnf(c_0_38,plain,
enc(inv(inv(X1)),X2) = enc(X1,X2),
inference(spm,[status(thm)],[c_0_32,c_0_32]) ).
cnf(c_0_39,plain,
( public(enc(xor(km,data),X1))
| ~ public(enc(xor(pin,kek),X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35])]) ).
cnf(c_0_40,plain,
public(enc(xor(pin,kek),pp)),
inference(rw,[status(thm)],[c_0_36,c_0_17]) ).
fof(c_0_41,negated_conjecture,
~ public(enc(pp,a)),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[co1])]) ).
cnf(c_0_42,plain,
( public(enc(X1,X2))
| ~ public(enc(xor(km,data),X1))
| ~ public(X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_32]),c_0_38]) ).
cnf(c_0_43,plain,
public(enc(xor(km,data),pp)),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
~ public(enc(pp,a)),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_45,plain,
( public(enc(pp,X1))
| ~ public(X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_46,plain,
public(a),
inference(split_conjunct,[status(thm)],[initial_knowledge8]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_46])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV234+2 : 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
% 0.17/0.34 % Computer : n019.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue May 5 04:58:29 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.20/0.35 % start to proof: theBenchmark
% 1.41/1.80 % Version : CSE_E---1.7
% 1.41/1.80 % Problem : theBenchmark.p
% 1.41/1.80 % SZS status Theorem for theBenchmark.p
% 1.41/1.80 % SZS output start CNFRefutation
% See solution above
% 1.41/1.80 % Total time : 1.419s
%------------------------------------------------------------------------------