%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW957+1 : TPTP v9.3.1. Released v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 : Tue Sep 29 01:38:05 PM UTC 2026
% Result : Theorem 0.68s 0.97s
% Output : Refutation 2.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of formulae : 81 ( 30 unt; 2 def)
% Number of atoms : 144 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 117 ( 54 ~; 50 |; 2 &)
% ( 2 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 5 con; 0-2 aty)
% Number of variables : 87 ( 0 sgn 87 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f46,axiom,
! [X0,X1] : constr_split(constr_concat(X0,X1)) = tuple_2(X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).
fof(f49,axiom,
! [X0] : constr_xor(X0,X0) = constr_ZERO,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax48) ).
fof(f50,axiom,
! [X0] : constr_xor(X0,constr_ZERO) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
fof(f51,axiom,
! [X0,X1] : constr_xor(X0,X1) = constr_xor(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax50) ).
fof(f52,axiom,
! [X0,X1,X2] : constr_xor(X0,constr_xor(X1,X2)) = constr_xor(constr_xor(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).
fof(f53,axiom,
! [X0,X1] :
( ( pred_attacker(X0)
& pred_attacker(X1) )
=> pred_attacker(constr_xor(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
fof(f55,axiom,
! [X0] :
( pred_attacker(X0)
=> pred_attacker(constr_split(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax54) ).
fof(f59,axiom,
! [X0,X1] :
( pred_attacker(tuple_enc_oracle_out_2(X0,X1))
=> pred_attacker(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
fof(f60,axiom,
! [X0] :
( pred_attacker(X0)
=> pred_attacker(tuple_enc_oracle_in_1(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax59) ).
fof(f62,axiom,
! [X0,X1] :
( ( pred_attacker(X0)
& pred_attacker(X1) )
=> pred_attacker(constr_concat(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax61) ).
fof(f69,axiom,
pred_attacker(constr_CONST_0x30),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax68) ).
fof(f70,axiom,
! [X0] :
( pred_attacker(X0)
=> pred_attacker(constr_C(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69) ).
fof(f73,axiom,
! [X0,X1] :
( pred_attacker(tuple_B_out_1(X0,X1))
=> pred_attacker(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax72) ).
fof(f75,axiom,
! [X0,X1] :
( pred_attacker(tuple_2(X0,X1))
=> pred_attacker(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax74) ).
fof(f82,axiom,
! [X0] :
( pred_attacker(tuple_enc_oracle_in_1(X0))
=> pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_concat(X0,constr_C(X0)),constr_RC4(name_v,name_Kab)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax81) ).
fof(f83,axiom,
pred_attacker(tuple_B_out_1(name_v,constr_xor(constr_concat(name_objective,constr_C(name_objective)),constr_RC4(name_v,name_Kab)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax82) ).
fof(f84,conjecture,
pred_attacker(name_objective),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co0) ).
fof(f85,negated_conjecture,
~ pred_attacker(name_objective),
inference(negated_conjecture,[status(cth)],[f84]) ).
fof(f86,plain,
~ pred_attacker(name_objective),
inference(flattening,[],[f85]) ).
fof(f88,plain,
! [X0,X1] :
( pred_attacker(constr_xor(X0,X1))
| ~ pred_attacker(X0)
| ~ pred_attacker(X1) ),
inference(ennf_transformation,[],[f53]) ).
fof(f89,plain,
! [X0,X1] :
( pred_attacker(constr_xor(X0,X1))
| ~ pred_attacker(X0)
| ~ pred_attacker(X1) ),
inference(flattening,[],[f88]) ).
fof(f90,plain,
! [X0] :
( pred_attacker(constr_split(X0))
| ~ pred_attacker(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f94,plain,
! [X0,X1] :
( pred_attacker(X1)
| ~ pred_attacker(tuple_enc_oracle_out_2(X0,X1)) ),
inference(ennf_transformation,[],[f59]) ).
fof(f95,plain,
! [X0] :
( pred_attacker(tuple_enc_oracle_in_1(X0))
| ~ pred_attacker(X0) ),
inference(ennf_transformation,[],[f60]) ).
fof(f97,plain,
! [X0,X1] :
( pred_attacker(constr_concat(X0,X1))
| ~ pred_attacker(X0)
| ~ pred_attacker(X1) ),
inference(ennf_transformation,[],[f62]) ).
fof(f98,plain,
! [X0,X1] :
( pred_attacker(constr_concat(X0,X1))
| ~ pred_attacker(X0)
| ~ pred_attacker(X1) ),
inference(flattening,[],[f97]) ).
fof(f101,plain,
! [X0] :
( pred_attacker(constr_C(X0))
| ~ pred_attacker(X0) ),
inference(ennf_transformation,[],[f70]) ).
fof(f105,plain,
! [X0,X1] :
( pred_attacker(X1)
| ~ pred_attacker(tuple_B_out_1(X0,X1)) ),
inference(ennf_transformation,[],[f73]) ).
fof(f108,plain,
! [X0,X1] :
( pred_attacker(X0)
| ~ pred_attacker(tuple_2(X0,X1)) ),
inference(ennf_transformation,[],[f75]) ).
fof(f114,plain,
! [X0] :
( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_concat(X0,constr_C(X0)),constr_RC4(name_v,name_Kab))))
| ~ pred_attacker(tuple_enc_oracle_in_1(X0)) ),
inference(ennf_transformation,[],[f82]) ).
fof(f160,plain,
! [X0,X1] : constr_split(constr_concat(X0,X1)) = tuple_2(X0,X1),
inference(cnf_transformation,[],[f46]) ).
fof(f163,plain,
! [X0] : constr_ZERO = constr_xor(X0,X0),
inference(cnf_transformation,[],[f49]) ).
fof(f164,plain,
! [X0] : constr_xor(X0,constr_ZERO) = X0,
inference(cnf_transformation,[],[f50]) ).
fof(f165,plain,
! [X0,X1] : constr_xor(X0,X1) = constr_xor(X1,X0),
inference(cnf_transformation,[],[f51]) ).
fof(f166,plain,
! [X2,X0,X1] : constr_xor(X0,constr_xor(X1,X2)) = constr_xor(constr_xor(X0,X1),X2),
inference(cnf_transformation,[],[f52]) ).
fof(f167,plain,
! [X0,X1] :
( pred_attacker(constr_xor(X0,X1))
| ~ pred_attacker(X0)
| ~ pred_attacker(X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f169,plain,
! [X0] :
( pred_attacker(constr_split(X0))
| ~ pred_attacker(X0) ),
inference(cnf_transformation,[],[f90]) ).
fof(f173,plain,
! [X0,X1] :
( ~ pred_attacker(tuple_enc_oracle_out_2(X0,X1))
| pred_attacker(X1) ),
inference(cnf_transformation,[],[f94]) ).
fof(f174,plain,
! [X0] :
( pred_attacker(tuple_enc_oracle_in_1(X0))
| ~ pred_attacker(X0) ),
inference(cnf_transformation,[],[f95]) ).
fof(f176,plain,
! [X0,X1] :
( pred_attacker(constr_concat(X0,X1))
| ~ pred_attacker(X0)
| ~ pred_attacker(X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f183,plain,
pred_attacker(constr_CONST_0x30),
inference(cnf_transformation,[],[f69]) ).
fof(f184,plain,
! [X0] :
( pred_attacker(constr_C(X0))
| ~ pred_attacker(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f187,plain,
! [X0,X1] :
( ~ pred_attacker(tuple_B_out_1(X0,X1))
| pred_attacker(X1) ),
inference(cnf_transformation,[],[f105]) ).
fof(f189,plain,
! [X0,X1] :
( ~ pred_attacker(tuple_2(X0,X1))
| pred_attacker(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f195,plain,
! [X0] :
( ~ pred_attacker(tuple_enc_oracle_in_1(X0))
| pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_concat(X0,constr_C(X0)),constr_RC4(name_v,name_Kab)))) ),
inference(cnf_transformation,[],[f114]) ).
fof(f196,plain,
pred_attacker(tuple_B_out_1(name_v,constr_xor(constr_concat(name_objective,constr_C(name_objective)),constr_RC4(name_v,name_Kab)))),
inference(cnf_transformation,[],[f83]) ).
fof(f197,plain,
~ pred_attacker(name_objective),
inference(cnf_transformation,[],[f86]) ).
fof(f207,plain,
pred_attacker(constr_xor(constr_concat(name_objective,constr_C(name_objective)),constr_RC4(name_v,name_Kab))),
inference(resolution,[],[f196,f187]) ).
fof(f209,plain,
! [X0] :
( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_concat(X0,constr_C(X0)),constr_RC4(name_v,name_Kab))))
| ~ pred_attacker(X0) ),
inference(resolution,[],[f195,f174]) ).
fof(f213,plain,
! [X0] : constr_xor(constr_ZERO,X0) = X0,
inference(superposition,[],[f165,f164]) ).
fof(f226,plain,
! [X0,X1] :
( pred_attacker(tuple_2(X0,X1))
| ~ pred_attacker(constr_concat(X0,X1)) ),
inference(superposition,[],[f169,f160]) ).
fof(f227,plain,
pred_attacker(constr_xor(constr_RC4(name_v,name_Kab),constr_concat(name_objective,constr_C(name_objective)))),
inference(forward_demodulation,[],[f207,f165]) ).
fof(f242,plain,
! [X0,X1] : constr_xor(X0,constr_xor(X0,X1)) = constr_xor(constr_ZERO,X1),
inference(superposition,[],[f166,f163]) ).
fof(f259,plain,
! [X0,X1] : constr_xor(X0,constr_xor(X0,X1)) = X1,
inference(forward_demodulation,[],[f242,f213]) ).
fof(f261,plain,
! [X0] :
( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_RC4(name_v,name_Kab),constr_concat(X0,constr_C(X0)))))
| ~ pred_attacker(X0) ),
inference(forward_demodulation,[],[f209,f165]) ).
fof(f263,plain,
! [X0,X1] : constr_xor(X1,constr_xor(X0,X1)) = X0,
inference(superposition,[],[f259,f165]) ).
fof(f272,plain,
! [X0,X1] :
( ~ pred_attacker(constr_xor(X1,X0))
| ~ pred_attacker(X1)
| pred_attacker(X0) ),
inference(superposition,[],[f167,f259]) ).
fof(f280,plain,
! [X0] :
( pred_attacker(constr_xor(constr_RC4(name_v,name_Kab),constr_concat(X0,constr_C(X0))))
| ~ pred_attacker(X0) ),
inference(resolution,[],[f261,f173]) ).
fof(f298,plain,
! [X0,X1] :
( ~ pred_attacker(constr_xor(X0,X1))
| ~ pred_attacker(X1)
| pred_attacker(X0) ),
inference(superposition,[],[f167,f263]) ).
fof(f328,plain,
! [X0,X1] :
( ~ pred_attacker(constr_concat(X0,X1))
| pred_attacker(X0) ),
inference(resolution,[],[f226,f189]) ).
fof(f336,plain,
( ~ pred_attacker(constr_RC4(name_v,name_Kab))
| pred_attacker(constr_concat(name_objective,constr_C(name_objective))) ),
inference(resolution,[],[f272,f227]) ).
fof(f349,definition,
( spl0_1
<=> pred_attacker(constr_concat(name_objective,constr_C(name_objective))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f351,plain,
( pred_attacker(constr_concat(name_objective,constr_C(name_objective)))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f349]) ).
fof(f353,definition,
( spl0_2
<=> pred_attacker(constr_RC4(name_v,name_Kab)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f355,plain,
( ~ pred_attacker(constr_RC4(name_v,name_Kab))
| spl0_2 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f356,plain,
( spl0_1
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f336,f353,f349]) ).
fof(f707,plain,
! [X0] :
( ~ pred_attacker(X0)
| ~ pred_attacker(constr_concat(X0,constr_C(X0)))
| pred_attacker(constr_RC4(name_v,name_Kab)) ),
inference(resolution,[],[f280,f298]) ).
fof(f713,plain,
! [X0] :
( ~ pred_attacker(constr_concat(X0,constr_C(X0)))
| pred_attacker(constr_RC4(name_v,name_Kab)) ),
inference(forward_subsumption_resolution,[],[f707,f328]) ).
fof(f716,plain,
( ! [X0] : ~ pred_attacker(constr_concat(X0,constr_C(X0)))
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f713,f355]) ).
fof(f717,plain,
( ! [X0] :
( ~ pred_attacker(X0)
| ~ pred_attacker(constr_C(X0)) )
| spl0_2 ),
inference(resolution,[],[f716,f176]) ).
fof(f721,plain,
( ! [X0] : ~ pred_attacker(X0)
| spl0_2 ),
inference(forward_subsumption_resolution,[],[f717,f184]) ).
fof(f752,plain,
( $false
| spl0_2 ),
inference(resolution,[],[f721,f183]) ).
fof(f794,plain,
spl0_2,
inference(avatar_contradiction_clause,[],[f752]) ).
fof(f1131,plain,
( pred_attacker(name_objective)
| ~ spl0_1 ),
inference(resolution,[],[f351,f328]) ).
fof(f1133,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f1131,f197]) ).
fof(f1134,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f1133]) ).
cnf(s1,plain,
( spl0_1
| ~ spl0_2 ),
inference(sat_conversion,[],[f356]) ).
cnf(s16,plain,
spl0_2,
inference(sat_conversion,[],[f794]) ).
cnf(s20,plain,
~ spl0_1,
inference(sat_conversion,[],[f1134]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s1,s16,s20]) ).
fof(f1135,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW957+1 : TPTP v9.3.1. Released v7.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n013.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 14:47:21 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.68/0.97 % (1236490)Detected formulas, will run a generic FOF schedule.
% 0.68/0.97 % (1236613)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=344822670:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.68/0.97 % (1236613)First to succeed.
% 0.68/0.97 % (1236613)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1236490"
% 0.68/0.97 % (1236612)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1964069969:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.68/0.97 % (1236611)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4097293754:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.68/0.97 % (1236610)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=360241127:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.68/0.97 % (1236608)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=2142522643:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.68/0.97 % (1236609)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=3590169806:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.68/0.97 % (1236611)Refutation not found, incomplete strategy
% 0.68/0.97 % (1236611)------------------------------
% 0.68/0.97 % (1236611)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.68/0.97 % (1236611)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.97 % (1236611)CaDiCaL version: 2.1.3
% 0.68/0.97 % (1236611)Termination reason: Refutation not found, incomplete strategy
% 0.68/0.97 % (1236611)Time elapsed: 0.001 s
% 0.68/0.97 % (1236611)Peak memory usage: 87 MB
% 0.68/0.97 % (1236612)Refutation not found, incomplete strategy
% 0.68/0.97 % (1236612)------------------------------
% 0.68/0.97 % (1236612)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.68/0.97 % (1236612)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.97 % (1236612)CaDiCaL version: 2.1.3
% 0.68/0.97 % (1236612)Termination reason: Refutation not found, incomplete strategy
% 0.68/0.97 % (1236612)Time elapsed: 0.001 s
% 0.68/0.97 % (1236612)Peak memory usage: 87 MB
% 0.68/0.97 % (1236614)dis-21_1_sil=8000:lcm=predicate:random_seed=2609108090:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.68/0.97 % (1236614)Refutation not found, incomplete strategy
% 0.68/0.97 % (1236614)------------------------------
% 0.68/0.97 % (1236614)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.68/0.97 % (1236614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.68/0.97 % (1236614)CaDiCaL version: 2.1.3
% 0.68/0.97 % (1236614)Termination reason: Refutation not found, incomplete strategy
% 0.68/0.97 % (1236614)Time elapsed: 0.003 s
% 0.68/0.97 % (1236614)Peak memory usage: 88 MB
% 0.68/0.97 % (1236614)Instructions burned: 4 (million)
% 0.68/0.97 % (1236613)Refutation found. Thanks to Tanya!
% 0.68/0.97 % SZS status Theorem for theBenchmark
% 0.68/0.97 % SZS output start Proof for theBenchmark
% See solution above
% 2.61/1.07 % (1236613)------------------------------
% 2.61/1.07 % (1236613)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.61/1.07 % (1236613)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.61/1.07 % (1236613)CaDiCaL version: 2.1.3
% 2.61/1.07 % (1236613)Termination reason: Refutation
% 2.61/1.07 % (1236613)Time elapsed: 0.014 s
% 2.61/1.07 % (1236613)Peak memory usage: 90 MB
% 2.61/1.07 % (1236613)Instructions burned: 37 (million)
% 2.61/1.07 % (1236613)------------------------------
% 2.61/1.07 % (1236613)------------------------------
% 2.61/1.07 % (1236490)Success in time 0.283 s
% 2.61/1.07 % Vampire exiting
%------------------------------------------------------------------------------