%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SWW957+1 : TPTP v9.3.1. Released v7.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 01:45:15 PM UTC 2026
% Result : Theorem 0.20s 0.29s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 21
% Syntax : Number of formulae : 89 ( 40 unt; 4 def)
% Number of atoms : 143 ( 22 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 102 ( 48 ~; 42 |; 1 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-2 aty)
% Number of variables : 81 ( 0 sgn 81 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f46,axiom,
! [X0,X1] : constr_split(constr_concat(X0,X1)) = tuple_2(X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).
fof(f47,axiom,
! [X0,X1,X2,X3] : constr_xor(constr_concat(X0,X2),constr_concat(X1,X3)) = constr_concat(constr_xor(X0,X1),constr_xor(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).
fof(f48,axiom,
! [X0,X1] : constr_C(constr_xor(X0,X1)) = constr_xor(constr_C(X0),constr_C(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax47) ).
fof(f49,axiom,
! [X0] : constr_xor(X0,X0) = constr_ZERO,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax48) ).
fof(f50,axiom,
! [X0] : constr_xor(X0,constr_ZERO) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49) ).
fof(f51,axiom,
! [X0,X1] : constr_xor(X0,X1) = constr_xor(X1,X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax51) ).
fof(f53,axiom,
! [X0,X1] :
( ( pred_attacker(X0)
& pred_attacker(X1) )
=> pred_attacker(constr_xor(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).
fof(f55,axiom,
! [X0] :
( pred_attacker(X0)
=> pred_attacker(constr_split(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54) ).
fof(f59,axiom,
! [X0,X1] :
( pred_attacker(tuple_enc_oracle_out_2(X0,X1))
=> pred_attacker(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
fof(f60,axiom,
! [X0] :
( pred_attacker(X0)
=> pred_attacker(tuple_enc_oracle_in_1(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax59) ).
fof(f63,axiom,
pred_attacker(constr_ZERO),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).
fof(f73,axiom,
! [X0,X1] :
( pred_attacker(tuple_B_out_1(X0,X1))
=> pred_attacker(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).
fof(f75,axiom,
! [X0,X1] :
( pred_attacker(tuple_2(X0,X1))
=> pred_attacker(X0) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',ax82) ).
fof(f84,conjecture,
pred_attacker(name_objective),
file('/export/starexec/sandbox2/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(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(f161,plain,
! [X2,X3,X0,X1] : constr_xor(constr_concat(X0,X2),constr_concat(X1,X3)) = constr_concat(constr_xor(X0,X1),constr_xor(X2,X3)),
inference(cnf_transformation,[],[f47]) ).
fof(f162,plain,
! [X0,X1] : constr_C(constr_xor(X0,X1)) = constr_xor(constr_C(X0),constr_C(X1)),
inference(cnf_transformation,[],[f48]) ).
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(f177,plain,
pred_attacker(constr_ZERO),
inference(cnf_transformation,[],[f63]) ).
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(X0)
| ~ pred_attacker(tuple_2(X0,X1)) ),
inference(cnf_transformation,[],[f108]) ).
fof(f195,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(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(f199,plain,
! [X0,X1] :
( ~ pred_attacker(constr_split(constr_concat(X0,X1)))
| pred_attacker(X0) ),
inference(definition_unfolding,[],[f189,f160]) ).
fof(f202,plain,
! [X0] : constr_xor(constr_ZERO,X0) = X0,
inference(superposition,[],[f165,f164]) ).
fof(f212,plain,
! [X0,X1] :
( ~ pred_attacker(constr_concat(X0,X1))
| pred_attacker(X0) ),
inference(resolution,[],[f199,f169]) ).
fof(f231,plain,
! [X0] : constr_ZERO = constr_C(constr_xor(X0,X0)),
inference(superposition,[],[f163,f162]) ).
fof(f235,plain,
constr_ZERO = constr_C(constr_ZERO),
inference(forward_demodulation,[],[f231,f163]) ).
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,f202]) ).
fof(f261,plain,
pred_attacker(tuple_B_out_1(name_v,constr_xor(constr_RC4(name_v,name_Kab),constr_concat(name_objective,constr_C(name_objective))))),
inference(forward_demodulation,[],[f196,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,
pred_attacker(constr_xor(constr_RC4(name_v,name_Kab),constr_concat(name_objective,constr_C(name_objective)))),
inference(resolution,[],[f261,f187]) ).
fof(f282,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(tuple_enc_oracle_in_1(X0)) ),
inference(forward_demodulation,[],[f195,f165]) ).
fof(f305,plain,
( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_RC4(name_v,name_Kab),constr_concat(constr_ZERO,constr_ZERO))))
| ~ pred_attacker(tuple_enc_oracle_in_1(constr_ZERO)) ),
inference(superposition,[],[f282,f235]) ).
fof(f306,plain,
( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_concat(constr_ZERO,constr_ZERO),constr_RC4(name_v,name_Kab))))
| ~ pred_attacker(tuple_enc_oracle_in_1(constr_ZERO)) ),
inference(forward_demodulation,[],[f305,f165]) ).
fof(f308,definition,
( spl0_1
<=> pred_attacker(tuple_enc_oracle_in_1(constr_ZERO)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f310,plain,
( ~ pred_attacker(tuple_enc_oracle_in_1(constr_ZERO))
| spl0_1 ),
inference(avatar_component_clause,[],[f308]) ).
fof(f312,definition,
( spl0_2
<=> pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_concat(constr_ZERO,constr_ZERO),constr_RC4(name_v,name_Kab)))) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f314,plain,
( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_concat(constr_ZERO,constr_ZERO),constr_RC4(name_v,name_Kab))))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f315,plain,
( ~ spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f306,f312,f308]) ).
fof(f316,plain,
( ~ pred_attacker(constr_ZERO)
| spl0_1 ),
inference(resolution,[],[f310,f174]) ).
fof(f317,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f316,f177]) ).
fof(f318,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f317]) ).
fof(f322,plain,
! [X0,X1] : constr_ZERO = constr_concat(constr_xor(X0,X0),constr_xor(X1,X1)),
inference(superposition,[],[f163,f161]) ).
fof(f331,plain,
! [X0] : constr_ZERO = constr_concat(constr_xor(X0,X0),constr_ZERO),
inference(forward_demodulation,[],[f322,f163]) ).
fof(f335,plain,
constr_ZERO = constr_concat(constr_ZERO,constr_ZERO),
inference(forward_demodulation,[],[f331,f163]) ).
fof(f367,plain,
( ~ pred_attacker(constr_RC4(name_v,name_Kab))
| pred_attacker(constr_concat(name_objective,constr_C(name_objective))) ),
inference(resolution,[],[f280,f272]) ).
fof(f369,definition,
( spl0_3
<=> pred_attacker(constr_concat(name_objective,constr_C(name_objective))) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f371,plain,
( pred_attacker(constr_concat(name_objective,constr_C(name_objective)))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f373,definition,
( spl0_4
<=> pred_attacker(constr_RC4(name_v,name_Kab)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f376,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f367,f373,f369]) ).
fof(f462,plain,
( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_xor(constr_ZERO,constr_RC4(name_v,name_Kab))))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f314,f335]) ).
fof(f463,plain,
( pred_attacker(tuple_enc_oracle_out_2(name_v,constr_RC4(name_v,name_Kab)))
| ~ spl0_2 ),
inference(forward_demodulation,[],[f462,f202]) ).
fof(f464,plain,
( pred_attacker(constr_RC4(name_v,name_Kab))
| ~ spl0_2 ),
inference(resolution,[],[f463,f173]) ).
fof(f469,plain,
( spl0_4
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f464,f312,f373]) ).
fof(f599,plain,
( pred_attacker(name_objective)
| ~ spl0_3 ),
inference(resolution,[],[f371,f212]) ).
fof(f600,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f599,f197]) ).
fof(f601,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f600]) ).
cnf(s1,plain,
( ~ spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f315]) ).
cnf(s2,plain,
spl0_1,
inference(sat_conversion,[],[f318]) ).
cnf(s3,plain,
( spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f376]) ).
cnf(s7,plain,
( ~ spl0_2
| spl0_4 ),
inference(sat_conversion,[],[f469]) ).
cnf(s8,plain,
~ spl0_3,
inference(sat_conversion,[],[f601]) ).
cnf(s9,plain,
~ spl0_4,
inference(rat,[],[s3,s8]) ).
cnf(s10,plain,
~ spl0_2,
inference(rat,[],[s7,s9]) ).
cnf(s11,plain,
$false,
inference(rat,[],[s1,s10,s2]) ).
fof(f602,plain,
$false,
inference(avatar_sat_refutation,[],[s11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW957+1 : TPTP v9.3.1. Released v7.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n013.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 14:47:21 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.29 % (1236346)Will run a generic schedule for satisfiability detection.
% 0.20/0.29 % (1236372)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2397952174:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.20/0.29 % (1236367)% WARNING: option uhcvi not known.
% 0.20/0.29 % (1236366)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1142688976_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.29 % (1236367)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=942117218:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.29 % (1236371)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2355569569:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.29 % (1236369)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3272348216:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.29 % (1236370)dis+10_1_sil=32000:sp=arity:random_seed=2786465377:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.29 % (1236373)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1474800195:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.20/0.29 % Detected minimum model sizes of [10]
% 0.20/0.29 % Detected maximum model sizes of [max]
% 0.20/0.29 % TRYING [10]
% 0.20/0.29 % (1236370) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1236346-1236370"...
% 0.20/0.29 % (1236370)...printing done.
% 0.20/0.29 % (1236370)Refutation found. Thanks to Tanya!
% 0.20/0.29 % SZS status Theorem for theBenchmark
% 0.20/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.29 % (1236370)------------------------------
% 0.20/0.29 % (1236370)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.29 % (1236370)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.29 % (1236370)CaDiCaL version: 2.1.3
% 0.20/0.29 % (1236370)Termination reason: Refutation
% 0.20/0.29 % (1236370)Time elapsed: 0.013 s
% 0.20/0.29 % (1236370)Peak memory usage: 12 MB
% 0.20/0.29 % (1236370)Instructions burned: 19 (million)
% 0.20/0.29 % (1236346)Success in time 0.06 s
% 0.20/0.29 % Vampire exiting
%------------------------------------------------------------------------------