TSTP Solution File: SWV233+1 by Beagle---0.9.51
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- Process Solution
%------------------------------------------------------------------------------
% File : Beagle---0.9.51
% Problem : SWV233+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n009.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 Aug 22 11:03:15 EDT 2023
% Result : Theorem 8.13s 3.05s
% Output : CNFRefutation 8.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 44
% Syntax : Number of formulae : 156 ( 53 unt; 27 typ; 0 def)
% Number of atoms : 323 ( 73 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 387 ( 193 ~; 163 |; 23 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 18 >; 8 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 9 con; 0-2 aty)
% Number of variables : 169 (; 169 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ knows > symmetric_encrypt > symmetric_decrypt > sign > mac > extract > encrypt > decrypt > concatenate > #nlpp > third > tail > second > kgen > inverse > head > hash > fourth > first > secret > s > n > k_s > k_ca > k_c > k_a > eol > c
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(extract,type,
extract: ( $i * $i ) > $i ).
tff(kgen,type,
kgen: $i > $i ).
tff(fourth,type,
fourth: $i > $i ).
tff(encrypt,type,
encrypt: ( $i * $i ) > $i ).
tff(knows,type,
knows: $i > $o ).
tff(k_c,type,
k_c: $i ).
tff(k_s,type,
k_s: $i ).
tff(inverse,type,
inverse: $i > $i ).
tff(s,type,
s: $i ).
tff(second,type,
second: $i > $i ).
tff(secret,type,
secret: $i ).
tff(decrypt,type,
decrypt: ( $i * $i ) > $i ).
tff(k_ca,type,
k_ca: $i ).
tff(k_a,type,
k_a: $i ).
tff(mac,type,
mac: ( $i * $i ) > $i ).
tff(sign,type,
sign: ( $i * $i ) > $i ).
tff(hash,type,
hash: $i > $i ).
tff(third,type,
third: $i > $i ).
tff(first,type,
first: $i > $i ).
tff(symmetric_decrypt,type,
symmetric_decrypt: ( $i * $i ) > $i ).
tff(n,type,
n: $i ).
tff(symmetric_encrypt,type,
symmetric_encrypt: ( $i * $i ) > $i ).
tff(tail,type,
tail: $i > $i ).
tff(concatenate,type,
concatenate: ( $i * $i ) > $i ).
tff(head,type,
head: $i > $i ).
tff(eol,type,
eol: $i ).
tff(c,type,
c: $i ).
tff(f_112,axiom,
( knows(k_ca)
& knows(inverse(k_a))
& knows(k_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',previous_knowledge) ).
tff(f_64,axiom,
! [E1,E2] :
( ( knows(E1)
& knows(E2) )
=> ( knows(concatenate(E1,E2))
& knows(encrypt(E1,E2))
& knows(symmetric_encrypt(E1,E2))
& knows(decrypt(E1,E2))
& knows(symmetric_decrypt(E1,E2))
& knows(extract(E1,E2))
& knows(sign(E1,E2)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',construct_message_1) ).
tff(f_93,axiom,
! [X] : ( first(X) = head(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first_axiom) ).
tff(f_89,axiom,
! [X,Y] : ( head(concatenate(X,Y)) = X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',head_axiom) ).
tff(f_91,axiom,
! [X,Y] : ( tail(concatenate(X,Y)) = Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tail_axiom) ).
tff(f_95,axiom,
! [X] : ( second(X) = head(tail(X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',second_axiom) ).
tff(f_86,axiom,
! [E,K] : ( extract(sign(E,inverse(K)),K) = E ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sign_axiom) ).
tff(f_135,axiom,
! [Init_1,Init_2,Init_3,Resp_1,Resp_2] :
( knows(concatenate(n,concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c)))))
& ( ( knows(Resp_1)
& knows(Resp_2)
& ( first(extract(Resp_2,k_ca)) = s )
& ( second(extract(decrypt(Resp_1,inverse(k_c)),second(extract(Resp_2,k_ca)))) = n ) )
=> knows(symmetric_encrypt(secret,first(extract(decrypt(Resp_1,inverse(k_c)),second(extract(Resp_2,k_ca)))))) )
& ( ( knows(Init_1)
& knows(Init_2)
& knows(Init_3)
& ( second(extract(Init_3,Init_2)) = Init_2 ) )
=> knows(concatenate(encrypt(sign(concatenate(kgen(Init_2),concatenate(Init_1,eol)),inverse(k_s)),Init_2),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',protocol) ).
tff(f_70,axiom,
! [E1,E2] :
( knows(concatenate(E1,E2))
=> ( knows(E1)
& knows(E2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',construct_message_2) ).
tff(f_31,axiom,
! [E1,E2] :
( ( knows(encrypt(E1,E2))
& knows(inverse(E2)) )
=> knows(E1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',encrypt_equation) ).
tff(f_79,axiom,
! [E] :
( knows(E)
=> ( knows(head(E))
& knows(tail(E))
& knows(hash(E)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',construct_message_3) ).
tff(f_97,axiom,
! [X] : ( third(X) = head(tail(tail(X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',third_axiom) ).
tff(f_99,axiom,
! [X] : ( fourth(X) = head(tail(tail(tail(X)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fourth_axiom) ).
tff(f_45,axiom,
! [E,K] :
( ( knows(sign(E,inverse(K)))
& knows(K) )
=> knows(E) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sign_equation) ).
tff(f_138,negated_conjecture,
~ knows(secret),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',attack) ).
tff(f_82,axiom,
! [E,K] : ( decrypt(encrypt(E,K),inverse(K)) = E ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',decrypt_axiom) ).
tff(f_38,axiom,
! [E1,E2] :
( ( knows(symmetric_encrypt(E1,E2))
& knows(E2) )
=> knows(E1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_encrypt_equation) ).
tff(c_52,plain,
knows(k_a),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_54,plain,
knows(inverse(k_a)),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_20,plain,
! [E1_7,E2_8] :
( knows(concatenate(E1_7,E2_8))
| ~ knows(E2_8)
| ~ knows(E1_7) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_42,plain,
! [X_22] : ( head(X_22) = first(X_22) ),
inference(cnfTransformation,[status(thm)],[f_93]) ).
tff(c_76,plain,
! [X_35,Y_36] : ( head(concatenate(X_35,Y_36)) = X_35 ),
inference(cnfTransformation,[status(thm)],[f_89]) ).
tff(c_88,plain,
! [X_35,Y_36] : ( first(concatenate(X_35,Y_36)) = X_35 ),
inference(superposition,[status(thm),theory(equality)],[c_42,c_76]) ).
tff(c_40,plain,
! [X_20,Y_21] : ( tail(concatenate(X_20,Y_21)) = Y_21 ),
inference(cnfTransformation,[status(thm)],[f_91]) ).
tff(c_101,plain,
! [X_40] : ( head(tail(X_40)) = second(X_40) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_113,plain,
! [X_20,Y_21] : ( second(concatenate(X_20,Y_21)) = head(Y_21) ),
inference(superposition,[status(thm),theory(equality)],[c_40,c_101]) ).
tff(c_119,plain,
! [X_20,Y_21] : ( second(concatenate(X_20,Y_21)) = first(Y_21) ),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_113]) ).
tff(c_8,plain,
! [E1_7,E2_8] :
( knows(sign(E1_7,E2_8))
| ~ knows(E2_8)
| ~ knows(E1_7) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_36,plain,
! [E_16,K_17] : ( extract(sign(E_16,inverse(K_17)),K_17) = E_16 ),
inference(cnfTransformation,[status(thm)],[f_86]) ).
tff(c_552,plain,
! [Init_2_105,Init_1_106,Init_3_107] :
( knows(concatenate(encrypt(sign(concatenate(kgen(Init_2_105),concatenate(Init_1_106,eol)),inverse(k_s)),Init_2_105),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| ( second(extract(Init_3_107,Init_2_105)) != Init_2_105 )
| ~ knows(Init_3_107)
| ~ knows(Init_2_105)
| ~ knows(Init_1_106) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_1943,plain,
! [K_203,Init_1_204,E_205] :
( knows(concatenate(encrypt(sign(concatenate(kgen(K_203),concatenate(Init_1_204,eol)),inverse(k_s)),K_203),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| ( second(E_205) != K_203 )
| ~ knows(sign(E_205,inverse(K_203)))
| ~ knows(K_203)
| ~ knows(Init_1_204) ),
inference(superposition,[status(thm),theory(equality)],[c_36,c_552]) ).
tff(c_1952,plain,
! [K_203,Init_1_204,E1_7] :
( knows(concatenate(encrypt(sign(concatenate(kgen(K_203),concatenate(Init_1_204,eol)),inverse(k_s)),K_203),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| ( second(E1_7) != K_203 )
| ~ knows(K_203)
| ~ knows(Init_1_204)
| ~ knows(inverse(K_203))
| ~ knows(E1_7) ),
inference(resolution,[status(thm)],[c_8,c_1943]) ).
tff(c_3478,plain,
! [E1_428,Init_1_429] :
( knows(concatenate(encrypt(sign(concatenate(kgen(second(E1_428)),concatenate(Init_1_429,eol)),inverse(k_s)),second(E1_428)),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| ~ knows(second(E1_428))
| ~ knows(Init_1_429)
| ~ knows(inverse(second(E1_428)))
| ~ knows(E1_428) ),
inference(reflexivity,[status(thm),theory(equality)],[c_1952]) ).
tff(c_24,plain,
! [E1_9,E2_10] :
( knows(E1_9)
| ~ knows(concatenate(E1_9,E2_10)) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_3527,plain,
! [E1_430,Init_1_431] :
( knows(encrypt(sign(concatenate(kgen(second(E1_430)),concatenate(Init_1_431,eol)),inverse(k_s)),second(E1_430)))
| ~ knows(second(E1_430))
| ~ knows(Init_1_431)
| ~ knows(inverse(second(E1_430)))
| ~ knows(E1_430) ),
inference(resolution,[status(thm)],[c_3478,c_24]) ).
tff(c_2,plain,
! [E1_1,E2_2] :
( knows(E1_1)
| ~ knows(inverse(E2_2))
| ~ knows(encrypt(E1_1,E2_2)) ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_3556,plain,
! [E1_432,Init_1_433] :
( knows(sign(concatenate(kgen(second(E1_432)),concatenate(Init_1_433,eol)),inverse(k_s)))
| ~ knows(second(E1_432))
| ~ knows(Init_1_433)
| ~ knows(inverse(second(E1_432)))
| ~ knows(E1_432) ),
inference(resolution,[status(thm)],[c_3527,c_2]) ).
tff(c_58,plain,
knows(concatenate(n,concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c))))),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_28,plain,
! [E_11] :
( knows(tail(E_11))
| ~ knows(E_11) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_137,plain,
! [X_44] : ( first(tail(X_44)) = second(X_44) ),
inference(superposition,[status(thm),theory(equality)],[c_101,c_42]) ).
tff(c_30,plain,
! [E_11] :
( knows(head(E_11))
| ~ knows(E_11) ),
inference(cnfTransformation,[status(thm)],[f_79]) ).
tff(c_65,plain,
! [E_11] :
( knows(first(E_11))
| ~ knows(E_11) ),
inference(demodulation,[status(thm),theory(equality)],[c_42,c_30]) ).
tff(c_344,plain,
! [X_69] :
( knows(second(X_69))
| ~ knows(tail(X_69)) ),
inference(superposition,[status(thm),theory(equality)],[c_137,c_65]) ).
tff(c_353,plain,
! [E_70] :
( knows(second(E_70))
| ~ knows(E_70) ),
inference(resolution,[status(thm)],[c_28,c_344]) ).
tff(c_359,plain,
! [Y_21,X_20] :
( knows(first(Y_21))
| ~ knows(concatenate(X_20,Y_21)) ),
inference(superposition,[status(thm),theory(equality)],[c_119,c_353]) ).
tff(c_514,plain,
knows(first(concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c))))),
inference(resolution,[status(thm)],[c_58,c_359]) ).
tff(c_526,plain,
knows(k_c),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_514]) ).
tff(c_18,plain,
! [E1_7,E2_8] :
( knows(encrypt(E1_7,E2_8))
| ~ knows(E2_8)
| ~ knows(E1_7) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_56,plain,
knows(k_ca),
inference(cnfTransformation,[status(thm)],[f_112]) ).
tff(c_22,plain,
! [E2_10,E1_9] :
( knows(E2_10)
| ~ knows(concatenate(E1_9,E2_10)) ),
inference(cnfTransformation,[status(thm)],[f_70]) ).
tff(c_528,plain,
knows(concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c)))),
inference(resolution,[status(thm)],[c_58,c_22]) ).
tff(c_551,plain,
knows(sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c))),
inference(resolution,[status(thm)],[c_528,c_22]) ).
tff(c_1945,plain,
! [Init_1_204] :
( knows(concatenate(encrypt(sign(concatenate(kgen(k_c),concatenate(Init_1_204,eol)),inverse(k_s)),k_c),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| ( second(concatenate(c,concatenate(k_c,eol))) != k_c )
| ~ knows(k_c)
| ~ knows(Init_1_204) ),
inference(resolution,[status(thm)],[c_551,c_1943]) ).
tff(c_2028,plain,
! [Init_1_219] :
( knows(concatenate(encrypt(sign(concatenate(kgen(k_c),concatenate(Init_1_219,eol)),inverse(k_s)),k_c),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| ~ knows(Init_1_219) ),
inference(demodulation,[status(thm),theory(equality)],[c_526,c_88,c_119,c_1945]) ).
tff(c_2048,plain,
! [Init_1_219] :
( knows(sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca)))
| ~ knows(Init_1_219) ),
inference(resolution,[status(thm)],[c_2028,c_22]) ).
tff(c_2049,plain,
! [Init_1_219] : ~ knows(Init_1_219),
inference(splitLeft,[status(thm)],[c_2048]) ).
tff(c_46,plain,
! [X_24] : ( head(tail(tail(X_24))) = third(X_24) ),
inference(cnfTransformation,[status(thm)],[f_97]) ).
tff(c_236,plain,
! [X_56] : ( head(tail(tail(tail(X_56)))) = fourth(X_56) ),
inference(cnfTransformation,[status(thm)],[f_99]) ).
tff(c_260,plain,
! [Y_21,X_20] : ( head(tail(tail(Y_21))) = fourth(concatenate(X_20,Y_21)) ),
inference(superposition,[status(thm),theory(equality)],[c_40,c_236]) ).
tff(c_266,plain,
! [X_20,Y_21] : ( fourth(concatenate(X_20,Y_21)) = third(Y_21) ),
inference(demodulation,[status(thm),theory(equality)],[c_46,c_260]) ).
tff(c_44,plain,
! [X_23] : ( head(tail(X_23)) = second(X_23) ),
inference(cnfTransformation,[status(thm)],[f_95]) ).
tff(c_245,plain,
! [X_56] : ( second(tail(tail(X_56))) = fourth(X_56) ),
inference(superposition,[status(thm),theory(equality)],[c_236,c_44]) ).
tff(c_419,plain,
! [X_80] :
( knows(fourth(X_80))
| ~ knows(tail(tail(X_80))) ),
inference(superposition,[status(thm),theory(equality)],[c_245,c_353]) ).
tff(c_428,plain,
! [X_81] :
( knows(fourth(X_81))
| ~ knows(tail(X_81)) ),
inference(resolution,[status(thm)],[c_28,c_419]) ).
tff(c_437,plain,
! [E_82] :
( knows(fourth(E_82))
| ~ knows(E_82) ),
inference(resolution,[status(thm)],[c_28,c_428]) ).
tff(c_440,plain,
! [Y_21,X_20] :
( knows(third(Y_21))
| ~ knows(concatenate(X_20,Y_21)) ),
inference(superposition,[status(thm),theory(equality)],[c_266,c_437]) ).
tff(c_546,plain,
knows(third(sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c)))),
inference(resolution,[status(thm)],[c_528,c_440]) ).
tff(c_2130,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2049,c_546]) ).
tff(c_2131,plain,
knows(sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))),
inference(splitRight,[status(thm)],[c_2048]) ).
tff(c_6,plain,
! [E_5,K_6] :
( knows(E_5)
| ~ knows(K_6)
| ~ knows(sign(E_5,inverse(K_6))) ),
inference(cnfTransformation,[status(thm)],[f_45]) ).
tff(c_2149,plain,
( knows(concatenate(s,concatenate(k_s,eol)))
| ~ knows(k_ca) ),
inference(resolution,[status(thm)],[c_2131,c_6]) ).
tff(c_2169,plain,
knows(concatenate(s,concatenate(k_s,eol))),
inference(demodulation,[status(thm),theory(equality)],[c_56,c_2149]) ).
tff(c_2193,plain,
knows(first(concatenate(k_s,eol))),
inference(resolution,[status(thm)],[c_2169,c_359]) ).
tff(c_2205,plain,
knows(k_s),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_2193]) ).
tff(c_10,plain,
! [E1_7,E2_8] :
( knows(extract(E1_7,E2_8))
| ~ knows(E2_8)
| ~ knows(E1_7) ),
inference(cnfTransformation,[status(thm)],[f_64]) ).
tff(c_64,plain,
~ knows(secret),
inference(cnfTransformation,[status(thm)],[f_138]) ).
tff(c_32,plain,
! [E_12,K_13] : ( decrypt(encrypt(E_12,K_13),inverse(K_13)) = E_12 ),
inference(cnfTransformation,[status(thm)],[f_82]) ).
tff(c_584,plain,
! [Resp_1_108,Resp_2_109] :
( knows(symmetric_encrypt(secret,first(extract(decrypt(Resp_1_108,inverse(k_c)),second(extract(Resp_2_109,k_ca))))))
| ( second(extract(decrypt(Resp_1_108,inverse(k_c)),second(extract(Resp_2_109,k_ca)))) != n )
| ( first(extract(Resp_2_109,k_ca)) != s )
| ~ knows(Resp_2_109)
| ~ knows(Resp_1_108) ),
inference(cnfTransformation,[status(thm)],[f_135]) ).
tff(c_591,plain,
! [E_12,Resp_2_109] :
( knows(symmetric_encrypt(secret,first(extract(E_12,second(extract(Resp_2_109,k_ca))))))
| ( second(extract(decrypt(encrypt(E_12,k_c),inverse(k_c)),second(extract(Resp_2_109,k_ca)))) != n )
| ( first(extract(Resp_2_109,k_ca)) != s )
| ~ knows(Resp_2_109)
| ~ knows(encrypt(E_12,k_c)) ),
inference(superposition,[status(thm),theory(equality)],[c_32,c_584]) ).
tff(c_624,plain,
! [E_110,Resp_2_111] :
( knows(symmetric_encrypt(secret,first(extract(E_110,second(extract(Resp_2_111,k_ca))))))
| ( second(extract(E_110,second(extract(Resp_2_111,k_ca)))) != n )
| ( first(extract(Resp_2_111,k_ca)) != s )
| ~ knows(Resp_2_111)
| ~ knows(encrypt(E_110,k_c)) ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_591]) ).
tff(c_4,plain,
! [E1_3,E2_4] :
( knows(E1_3)
| ~ knows(E2_4)
| ~ knows(symmetric_encrypt(E1_3,E2_4)) ),
inference(cnfTransformation,[status(thm)],[f_38]) ).
tff(c_627,plain,
! [E_110,Resp_2_111] :
( knows(secret)
| ~ knows(first(extract(E_110,second(extract(Resp_2_111,k_ca)))))
| ( second(extract(E_110,second(extract(Resp_2_111,k_ca)))) != n )
| ( first(extract(Resp_2_111,k_ca)) != s )
| ~ knows(Resp_2_111)
| ~ knows(encrypt(E_110,k_c)) ),
inference(resolution,[status(thm)],[c_624,c_4]) ).
tff(c_664,plain,
! [E_116,Resp_2_117] :
( ~ knows(first(extract(E_116,second(extract(Resp_2_117,k_ca)))))
| ( second(extract(E_116,second(extract(Resp_2_117,k_ca)))) != n )
| ( first(extract(Resp_2_117,k_ca)) != s )
| ~ knows(Resp_2_117)
| ~ knows(encrypt(E_116,k_c)) ),
inference(negUnitSimplification,[status(thm)],[c_64,c_627]) ).
tff(c_1872,plain,
! [E_190,Resp_2_191] :
( ( second(extract(E_190,second(extract(Resp_2_191,k_ca)))) != n )
| ( first(extract(Resp_2_191,k_ca)) != s )
| ~ knows(Resp_2_191)
| ~ knows(encrypt(E_190,k_c))
| ~ knows(extract(E_190,second(extract(Resp_2_191,k_ca)))) ),
inference(resolution,[status(thm)],[c_65,c_664]) ).
tff(c_1880,plain,
! [E_190,E_16] :
( ( second(extract(E_190,second(extract(sign(E_16,inverse(k_ca)),k_ca)))) != n )
| ( first(extract(sign(E_16,inverse(k_ca)),k_ca)) != s )
| ~ knows(sign(E_16,inverse(k_ca)))
| ~ knows(encrypt(E_190,k_c))
| ~ knows(extract(E_190,second(E_16))) ),
inference(superposition,[status(thm),theory(equality)],[c_36,c_1872]) ).
tff(c_1886,plain,
! [E_190,E_16] :
( ( second(extract(E_190,second(E_16))) != n )
| ( first(E_16) != s )
| ~ knows(sign(E_16,inverse(k_ca)))
| ~ knows(encrypt(E_190,k_c))
| ~ knows(extract(E_190,second(E_16))) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_36,c_1880]) ).
tff(c_2133,plain,
! [E_190] :
( ( second(extract(E_190,second(concatenate(s,concatenate(k_s,eol))))) != n )
| ( first(concatenate(s,concatenate(k_s,eol))) != s )
| ~ knows(encrypt(E_190,k_c))
| ~ knows(extract(E_190,second(concatenate(s,concatenate(k_s,eol))))) ),
inference(resolution,[status(thm)],[c_2131,c_1886]) ).
tff(c_2500,plain,
! [E_232] :
( ( second(extract(E_232,k_s)) != n )
| ~ knows(encrypt(E_232,k_c))
| ~ knows(extract(E_232,k_s)) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_119,c_88,c_88,c_119,c_2133]) ).
tff(c_2504,plain,
! [E1_7] :
( ( second(extract(E1_7,k_s)) != n )
| ~ knows(encrypt(E1_7,k_c))
| ~ knows(k_s)
| ~ knows(E1_7) ),
inference(resolution,[status(thm)],[c_10,c_2500]) ).
tff(c_2513,plain,
! [E1_233] :
( ( second(extract(E1_233,k_s)) != n )
| ~ knows(encrypt(E1_233,k_c))
| ~ knows(E1_233) ),
inference(demodulation,[status(thm),theory(equality)],[c_2205,c_2504]) ).
tff(c_2517,plain,
! [E1_7] :
( ( second(extract(E1_7,k_s)) != n )
| ~ knows(k_c)
| ~ knows(E1_7) ),
inference(resolution,[status(thm)],[c_18,c_2513]) ).
tff(c_2521,plain,
! [E1_234] :
( ( second(extract(E1_234,k_s)) != n )
| ~ knows(E1_234) ),
inference(demodulation,[status(thm),theory(equality)],[c_526,c_2517]) ).
tff(c_2525,plain,
! [E_16] :
( ( second(E_16) != n )
| ~ knows(sign(E_16,inverse(k_s))) ),
inference(superposition,[status(thm),theory(equality)],[c_36,c_2521]) ).
tff(c_3559,plain,
! [E1_432,Init_1_433] :
( ( second(concatenate(kgen(second(E1_432)),concatenate(Init_1_433,eol))) != n )
| ~ knows(second(E1_432))
| ~ knows(Init_1_433)
| ~ knows(inverse(second(E1_432)))
| ~ knows(E1_432) ),
inference(resolution,[status(thm)],[c_3556,c_2525]) ).
tff(c_3575,plain,
! [Init_1_433,E1_432] :
( ( n != Init_1_433 )
| ~ knows(second(E1_432))
| ~ knows(Init_1_433)
| ~ knows(inverse(second(E1_432)))
| ~ knows(E1_432) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_119,c_3559]) ).
tff(c_3602,plain,
! [E1_437] :
( ~ knows(second(E1_437))
| ~ knows(inverse(second(E1_437)))
| ~ knows(E1_437) ),
inference(splitLeft,[status(thm)],[c_3575]) ).
tff(c_3608,plain,
! [X_20,Y_21] :
( ~ knows(second(concatenate(X_20,Y_21)))
| ~ knows(inverse(first(Y_21)))
| ~ knows(concatenate(X_20,Y_21)) ),
inference(superposition,[status(thm),theory(equality)],[c_119,c_3602]) ).
tff(c_3657,plain,
! [Y_445,X_446] :
( ~ knows(first(Y_445))
| ~ knows(inverse(first(Y_445)))
| ~ knows(concatenate(X_446,Y_445)) ),
inference(demodulation,[status(thm),theory(equality)],[c_119,c_3608]) ).
tff(c_3665,plain,
! [X_35,Y_36,X_446] :
( ~ knows(first(concatenate(X_35,Y_36)))
| ~ knows(inverse(X_35))
| ~ knows(concatenate(X_446,concatenate(X_35,Y_36))) ),
inference(superposition,[status(thm),theory(equality)],[c_88,c_3657]) ).
tff(c_3670,plain,
! [X_447,X_448,Y_449] :
( ~ knows(X_447)
| ~ knows(inverse(X_447))
| ~ knows(concatenate(X_448,concatenate(X_447,Y_449))) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_3665]) ).
tff(c_3693,plain,
! [X_447,Y_449,E1_7] :
( ~ knows(X_447)
| ~ knows(inverse(X_447))
| ~ knows(concatenate(X_447,Y_449))
| ~ knows(E1_7) ),
inference(resolution,[status(thm)],[c_20,c_3670]) ).
tff(c_3707,plain,
! [E1_7] : ~ knows(E1_7),
inference(splitLeft,[status(thm)],[c_3693]) ).
tff(c_2047,plain,
! [Init_1_219] :
( knows(encrypt(sign(concatenate(kgen(k_c),concatenate(Init_1_219,eol)),inverse(k_s)),k_c))
| ~ knows(Init_1_219) ),
inference(resolution,[status(thm)],[c_2028,c_24]) ).
tff(c_595,plain,
! [Resp_1_108,E_16] :
( knows(symmetric_encrypt(secret,first(extract(decrypt(Resp_1_108,inverse(k_c)),second(E_16)))))
| ( second(extract(decrypt(Resp_1_108,inverse(k_c)),second(extract(sign(E_16,inverse(k_ca)),k_ca)))) != n )
| ( first(extract(sign(E_16,inverse(k_ca)),k_ca)) != s )
| ~ knows(sign(E_16,inverse(k_ca)))
| ~ knows(Resp_1_108) ),
inference(superposition,[status(thm),theory(equality)],[c_36,c_584]) ).
tff(c_705,plain,
! [Resp_1_121,E_122] :
( knows(symmetric_encrypt(secret,first(extract(decrypt(Resp_1_121,inverse(k_c)),second(E_122)))))
| ( second(extract(decrypt(Resp_1_121,inverse(k_c)),second(E_122))) != n )
| ( first(E_122) != s )
| ~ knows(sign(E_122,inverse(k_ca)))
| ~ knows(Resp_1_121) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_36,c_595]) ).
tff(c_718,plain,
! [Resp_1_121,Y_21,X_20] :
( knows(symmetric_encrypt(secret,first(extract(decrypt(Resp_1_121,inverse(k_c)),first(Y_21)))))
| ( second(extract(decrypt(Resp_1_121,inverse(k_c)),second(concatenate(X_20,Y_21)))) != n )
| ( first(concatenate(X_20,Y_21)) != s )
| ~ knows(sign(concatenate(X_20,Y_21),inverse(k_ca)))
| ~ knows(Resp_1_121) ),
inference(superposition,[status(thm),theory(equality)],[c_119,c_705]) ).
tff(c_2608,plain,
! [Resp_1_244,Y_245,X_246] :
( knows(symmetric_encrypt(secret,first(extract(decrypt(Resp_1_244,inverse(k_c)),first(Y_245)))))
| ( second(extract(decrypt(Resp_1_244,inverse(k_c)),first(Y_245))) != n )
| ( s != X_246 )
| ~ knows(sign(concatenate(X_246,Y_245),inverse(k_ca)))
| ~ knows(Resp_1_244) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_119,c_718]) ).
tff(c_2610,plain,
! [Resp_1_244] :
( knows(symmetric_encrypt(secret,first(extract(decrypt(Resp_1_244,inverse(k_c)),first(concatenate(k_s,eol))))))
| ( second(extract(decrypt(Resp_1_244,inverse(k_c)),first(concatenate(k_s,eol)))) != n )
| ~ knows(Resp_1_244) ),
inference(resolution,[status(thm)],[c_2131,c_2608]) ).
tff(c_2617,plain,
! [Resp_1_247] :
( knows(symmetric_encrypt(secret,first(extract(decrypt(Resp_1_247,inverse(k_c)),k_s))))
| ( second(extract(decrypt(Resp_1_247,inverse(k_c)),k_s)) != n )
| ~ knows(Resp_1_247) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_88,c_2610]) ).
tff(c_2624,plain,
! [E_12] :
( knows(symmetric_encrypt(secret,first(extract(E_12,k_s))))
| ( second(extract(decrypt(encrypt(E_12,k_c),inverse(k_c)),k_s)) != n )
| ~ knows(encrypt(E_12,k_c)) ),
inference(superposition,[status(thm),theory(equality)],[c_32,c_2617]) ).
tff(c_2629,plain,
! [E_248] :
( knows(symmetric_encrypt(secret,first(extract(E_248,k_s))))
| ( second(extract(E_248,k_s)) != n )
| ~ knows(encrypt(E_248,k_c)) ),
inference(demodulation,[status(thm),theory(equality)],[c_32,c_2624]) ).
tff(c_2636,plain,
! [E_16] :
( knows(symmetric_encrypt(secret,first(E_16)))
| ( second(extract(sign(E_16,inverse(k_s)),k_s)) != n )
| ~ knows(encrypt(sign(E_16,inverse(k_s)),k_c)) ),
inference(superposition,[status(thm),theory(equality)],[c_36,c_2629]) ).
tff(c_2661,plain,
! [E_251] :
( knows(symmetric_encrypt(secret,first(E_251)))
| ( second(E_251) != n )
| ~ knows(encrypt(sign(E_251,inverse(k_s)),k_c)) ),
inference(demodulation,[status(thm),theory(equality)],[c_36,c_2636]) ).
tff(c_2664,plain,
! [Init_1_219] :
( knows(symmetric_encrypt(secret,first(concatenate(kgen(k_c),concatenate(Init_1_219,eol)))))
| ( second(concatenate(kgen(k_c),concatenate(Init_1_219,eol))) != n )
| ~ knows(Init_1_219) ),
inference(resolution,[status(thm)],[c_2047,c_2661]) ).
tff(c_2669,plain,
! [Init_1_219] :
( knows(symmetric_encrypt(secret,kgen(k_c)))
| ( n != Init_1_219 )
| ~ knows(Init_1_219) ),
inference(demodulation,[status(thm),theory(equality)],[c_88,c_119,c_88,c_2664]) ).
tff(c_2674,plain,
~ knows(n),
inference(splitLeft,[status(thm)],[c_2669]) ).
tff(c_527,plain,
knows(n),
inference(resolution,[status(thm)],[c_58,c_24]) ).
tff(c_2676,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_2674,c_527]) ).
tff(c_2677,plain,
knows(symmetric_encrypt(secret,kgen(k_c))),
inference(splitRight,[status(thm)],[c_2669]) ).
tff(c_3792,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3707,c_2677]) ).
tff(c_3794,plain,
! [X_453,Y_454] :
( ~ knows(X_453)
| ~ knows(inverse(X_453))
| ~ knows(concatenate(X_453,Y_454)) ),
inference(splitRight,[status(thm)],[c_3693]) ).
tff(c_3838,plain,
! [E1_7,E2_8] :
( ~ knows(inverse(E1_7))
| ~ knows(E2_8)
| ~ knows(E1_7) ),
inference(resolution,[status(thm)],[c_20,c_3794]) ).
tff(c_3854,plain,
! [E1_459] :
( ~ knows(inverse(E1_459))
| ~ knows(E1_459) ),
inference(splitLeft,[status(thm)],[c_3838]) ).
tff(c_3857,plain,
~ knows(k_a),
inference(resolution,[status(thm)],[c_54,c_3854]) ).
tff(c_3861,plain,
$false,
inference(demodulation,[status(thm),theory(equality)],[c_52,c_3857]) ).
tff(c_3862,plain,
! [E2_8] : ~ knows(E2_8),
inference(splitRight,[status(thm)],[c_3838]) ).
tff(c_3957,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3862,c_2677]) ).
tff(c_3959,plain,
~ knows(n),
inference(splitRight,[status(thm)],[c_3575]) ).
tff(c_3961,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_3959,c_527]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV233+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox2/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox2/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n009.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 3 22:48:38 EDT 2023
% 0.13/0.35 % CPUTime :
% 8.13/3.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.13/3.07
% 8.13/3.07 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.41/3.11
% 8.41/3.11 Inference rules
% 8.41/3.11 ----------------------
% 8.41/3.11 #Ref : 3
% 8.41/3.11 #Sup : 766
% 8.41/3.11 #Fact : 0
% 8.41/3.11 #Define : 0
% 8.41/3.11 #Split : 15
% 8.41/3.11 #Chain : 0
% 8.41/3.11 #Close : 0
% 8.41/3.11
% 8.41/3.11 Ordering : KBO
% 8.41/3.11
% 8.41/3.11 Simplification rules
% 8.41/3.11 ----------------------
% 8.41/3.11 #Subsume : 947
% 8.41/3.11 #Demod : 599
% 8.41/3.11 #Tautology : 82
% 8.41/3.11 #SimpNegUnit : 486
% 8.41/3.11 #BackRed : 164
% 8.41/3.11
% 8.41/3.11 #Partial instantiations: 0
% 8.41/3.11 #Strategies tried : 1
% 8.41/3.11
% 8.41/3.11 Timing (in seconds)
% 8.41/3.11 ----------------------
% 8.41/3.11 Preprocessing : 0.54
% 8.41/3.11 Parsing : 0.29
% 8.41/3.11 CNF conversion : 0.03
% 8.41/3.11 Main loop : 1.35
% 8.41/3.11 Inferencing : 0.48
% 8.41/3.11 Reduction : 0.44
% 8.41/3.11 Demodulation : 0.31
% 8.41/3.11 BG Simplification : 0.04
% 8.41/3.11 Subsumption : 0.31
% 8.41/3.11 Abstraction : 0.04
% 8.41/3.11 MUC search : 0.00
% 8.41/3.11 Cooper : 0.00
% 8.41/3.11 Total : 1.95
% 8.41/3.11 Index Insertion : 0.00
% 8.41/3.11 Index Deletion : 0.00
% 8.41/3.11 Index Matching : 0.00
% 8.41/3.11 BG Taut test : 0.00
%------------------------------------------------------------------------------