%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : SWV234+2 : TPTP v9.0.0. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n007.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 : Wed Apr 9 09:29:49 PM UTC 2025
% Result : Theorem 49.42s 34.81s
% Output : CNFRefutation 49.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 48 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 75 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 52 ( 25 ~; 22 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-2 aty)
% Number of variables : 76 ( 76 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ public > xor > enc > #nlpp > kp > inv > z > pp > pin > km > kek > k3 > imp > data > a
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(enc,type,
enc: ( $i * $i ) > $i ).
tff(a,type,
a: $i ).
tff(kp,type,
kp: $i > $i ).
tff(pp,type,
pp: $i ).
tff(data,type,
data: $i ).
tff(inv,type,
inv: $i > $i ).
tff(xor,type,
xor: ( $i * $i ) > $i ).
tff(k3,type,
k3: $i ).
tff(z,type,
z: $i ).
tff(public,type,
public: $i > $o ).
tff(kek,type,
kek: $i ).
tff(imp,type,
imp: $i ).
tff(pin,type,
pin: $i ).
tff(km,type,
km: $i ).
tff(f_92,axiom,
public(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge8) ).
tff(f_89,axiom,
public(enc(xor(kek,pin),pp)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge5) ).
tff(f_86,axiom,
public(data),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge2) ).
tff(f_78,axiom,
! [U,V,W] : ( xor(U,V) = xor(V,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutes) ).
tff(f_80,axiom,
! [U,V,W] : ( xor(U,xor(V,W)) = xor(xor(U,V),W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_assosciative) ).
tff(f_84,axiom,
! [U,V,W] : ( xor(U,z) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_zero) ).
tff(f_82,axiom,
! [U,V,W] : ( xor(U,U) = z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_self_cancel) ).
tff(f_93,axiom,
public(enc(xor(km,imp),xor(kek,xor(pin,data)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge9) ).
tff(f_66,axiom,
! [U,V,W] :
( ( public(V)
& public(enc(xor(U,V),W))
& public(enc(xor(km,imp),U)) )
=> public(enc(xor(km,V),W)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_import_cmd) ).
tff(f_76,axiom,
! [U,V,W] : ( enc(U,enc(inv(U),V)) = V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_decrypt_cancel) ).
tff(f_58,axiom,
! [U,V] :
( ( public(U)
& public(V) )
=> public(enc(enc(inv(xor(data,km)),U),V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_data_cmd) ).
tff(f_96,negated_conjecture,
~ public(enc(pp,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
tff(c_40,plain,
public(a),
inference(cnfTransformation,[status(thm)],[f_92]) ).
tff(c_34,plain,
public(enc(xor(kek,pin),pp)),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_28,plain,
public(data),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_18,plain,
! [V_20,U_19] : ( xor(V_20,U_19) = xor(U_19,V_20) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_333,plain,
! [U_51,V_52,W_53] : ( xor(xor(U_51,V_52),W_53) = xor(U_51,xor(V_52,W_53)) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_1050,plain,
! [V_82,U_83,V_84] : ( xor(V_82,xor(U_83,V_84)) = xor(U_83,xor(V_84,V_82)) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_333]) ).
tff(c_75,plain,
! [V_34,U_35] : ( xor(V_34,U_35) = xor(U_35,V_34) ),
inference(cnfTransformation,[status(thm)],[f_78]) ).
tff(c_24,plain,
! [U_28] : ( xor(U_28,z) = U_28 ),
inference(cnfTransformation,[status(thm)],[f_84]) ).
tff(c_91,plain,
! [U_35] : ( xor(z,U_35) = U_35 ),
inference(superposition,[status(thm),theory(equality)],[c_75,c_24]) ).
tff(c_22,plain,
! [U_25] : ( xor(U_25,U_25) = z ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_382,plain,
! [U_25,W_53] : ( xor(U_25,xor(U_25,W_53)) = xor(z,W_53) ),
inference(superposition,[status(thm),theory(equality)],[c_22,c_333]) ).
tff(c_400,plain,
! [U_25,W_53] : ( xor(U_25,xor(U_25,W_53)) = W_53 ),
inference(demodulation,[status(thm),theory(equality)],[c_91,c_382]) ).
tff(c_1138,plain,
! [V_82,U_83,V_84] : ( xor(V_82,xor(U_83,xor(V_84,V_82))) = xor(U_83,V_84) ),
inference(superposition,[status(thm),theory(equality)],[c_1050,c_400]) ).
tff(c_1388,plain,
! [V_85,U_86,W_87] : ( xor(xor(V_85,U_86),W_87) = xor(U_86,xor(V_85,W_87)) ),
inference(superposition,[status(thm),theory(equality)],[c_18,c_333]) ).
tff(c_20,plain,
! [U_22,V_23,W_24] : ( xor(xor(U_22,V_23),W_24) = xor(U_22,xor(V_23,W_24)) ),
inference(cnfTransformation,[status(thm)],[f_80]) ).
tff(c_1448,plain,
! [V_85,U_86,W_87] : ( xor(V_85,xor(U_86,W_87)) = xor(U_86,xor(V_85,W_87)) ),
inference(superposition,[status(thm),theory(equality)],[c_1388,c_20]) ).
tff(c_42,plain,
public(enc(xor(km,imp),xor(kek,xor(pin,data)))),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_45,plain,
public(enc(xor(imp,km),xor(kek,xor(data,pin)))),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_18,c_42]) ).
tff(c_12,plain,
! [V_11,W_12,U_10] :
( public(enc(xor(km,V_11),W_12))
| ~ public(enc(xor(km,imp),U_10))
| ~ public(enc(xor(U_10,V_11),W_12))
| ~ public(V_11) ),
inference(cnfTransformation,[status(thm)],[f_66]) ).
tff(c_905,plain,
! [V_73,W_74,U_75] :
( public(enc(xor(km,V_73),W_74))
| ~ public(enc(xor(imp,km),U_75))
| ~ public(enc(xor(U_75,V_73),W_74))
| ~ public(V_73) ),
inference(demodulation,[status(thm),theory(equality)],[c_18,c_12]) ).
tff(c_907,plain,
! [V_73,W_74] :
( public(enc(xor(km,V_73),W_74))
| ~ public(enc(xor(xor(kek,xor(data,pin)),V_73),W_74))
| ~ public(V_73) ),
inference(resolution,[status(thm)],[c_45,c_905]) ).
tff(c_915,plain,
! [V_73,W_74] :
( public(enc(xor(km,V_73),W_74))
| ~ public(enc(xor(kek,xor(data,xor(pin,V_73))),W_74))
| ~ public(V_73) ),
inference(demodulation,[status(thm),theory(equality)],[c_20,c_20,c_907]) ).
tff(c_12845,plain,
! [V_165,W_166] :
( public(enc(xor(km,V_165),W_166))
| ~ public(enc(xor(data,xor(kek,xor(pin,V_165))),W_166))
| ~ public(V_165) ),
inference(demodulation,[status(thm),theory(equality)],[c_1448,c_915]) ).
tff(c_12881,plain,
! [W_166] :
( public(enc(xor(km,data),W_166))
| ~ public(enc(xor(kek,pin),W_166))
| ~ public(data) ),
inference(superposition,[status(thm),theory(equality)],[c_1138,c_12845]) ).
tff(c_100114,plain,
! [W_461] :
( public(enc(xor(data,km),W_461))
| ~ public(enc(xor(kek,pin),W_461)) ),
inference(demodulation,[status(thm),theory(equality)],[c_28,c_18,c_12881]) ).
tff(c_100132,plain,
public(enc(xor(data,km),pp)),
inference(resolution,[status(thm)],[c_34,c_100114]) ).
tff(c_16,plain,
! [U_16,V_17] : ( enc(U_16,enc(inv(U_16),V_17)) = V_17 ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_171,plain,
! [U_37,V_38] : ( enc(U_37,enc(inv(U_37),V_38)) = V_38 ),
inference(cnfTransformation,[status(thm)],[f_76]) ).
tff(c_182,plain,
! [U_37,V_17] : ( enc(inv(inv(U_37)),V_17) = enc(U_37,V_17) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_171]) ).
tff(c_765,plain,
! [U_62,V_63] :
( public(enc(enc(inv(xor(data,km)),U_62),V_63))
| ~ public(V_63)
| ~ public(U_62) ),
inference(cnfTransformation,[status(thm)],[f_58]) ).
tff(c_776,plain,
! [V_17,V_63] :
( public(enc(V_17,V_63))
| ~ public(V_63)
| ~ public(enc(inv(inv(xor(data,km))),V_17)) ),
inference(superposition,[status(thm),theory(equality)],[c_16,c_765]) ).
tff(c_782,plain,
! [V_17,V_63] :
( public(enc(V_17,V_63))
| ~ public(V_63)
| ~ public(enc(xor(data,km),V_17)) ),
inference(demodulation,[status(thm),theory(equality)],[c_182,c_776]) ).
tff(c_100169,plain,
! [V_462] :
( public(enc(pp,V_462))
| ~ public(V_462) ),
inference(resolution,[status(thm)],[c_100132,c_782]) ).
tff(c_44,plain,
~ public(enc(pp,a)),
inference(cnfTransformation,[status(thm)],[f_96]) ).
tff(c_100184,plain,
~ public(a),
inference(resolution,[status(thm)],[c_100169,c_44]) ).
tff(c_100197,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_40,c_100184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWV234+2 : TPTP v9.0.0. Released v3.2.0.
% 0.07/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.14/0.35 % Computer : n007.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Wed Apr 9 02:52:24 EDT 2025
% 0.14/0.35 % CPUTime :
% 49.42/34.81 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 49.42/34.82
% 49.42/34.82 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------