%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWW948+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 : n018.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 01:38:04 PM UTC 2026
% Result : Theorem 3.10s 1.10s
% Output : Refutation 3.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 18
% Syntax : Number of formulae : 75 ( 32 unt; 2 def)
% Number of atoms : 133 ( 11 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 119 ( 61 ~; 46 |; 2 &)
% ( 2 <=>; 8 =>; 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 : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 66 ( 0 sgn 66 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f67,axiom,
! [X0] : constr_xor(X0,X0) = constr_ZERO,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).
fof(f68,axiom,
! [X0] : constr_xor(X0,constr_ZERO) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax67) ).
fof(f69,axiom,
! [X0,X1] : constr_xor(X0,X1) = constr_xor(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax68) ).
fof(f70,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',ax69) ).
fof(f71,axiom,
! [X0,X1] :
( ( pred_attacker(X0)
& pred_attacker(X1) )
=> pred_attacker(constr_xor(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax70) ).
fof(f76,axiom,
! [X0,X1] :
( pred_attacker(tuple_knowledge_from_1st_round_out_2(X0,X1))
=> pred_attacker(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax75) ).
fof(f77,axiom,
! [X0,X1] :
( pred_attacker(tuple_knowledge_from_1st_round_out_2(X0,X1))
=> pred_attacker(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax76) ).
fof(f79,axiom,
! [X0] :
( pred_attacker(tuple_knowledge_from_1st_round_out_1(X0))
=> pred_attacker(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax78) ).
fof(f84,axiom,
! [X0] :
( pred_attacker(tuple_R_out_4(X0))
=> pred_attacker(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax83) ).
fof(f88,axiom,
! [X0] :
( pred_attacker(tuple_R_out_1(X0))
=> pred_attacker(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax87) ).
fof(f89,axiom,
! [X0,X1] :
( ( pred_attacker(X0)
& pred_attacker(X1) )
=> pred_attacker(tuple_R_in_2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax88) ).
fof(f102,axiom,
pred_attacker(tuple_knowledge_from_1st_round_out_1(name_r0x30_from_1st)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax101) ).
fof(f103,axiom,
pred_attacker(tuple_knowledge_from_1st_round_out_2(name_r1_from_1st,constr_h(constr_xor(constr_xor(name_r0x30_from_1st,name_r1_from_1st),name_k)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax102) ).
fof(f105,axiom,
pred_attacker(tuple_R_out_1(name_r0x30)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax104) ).
fof(f107,axiom,
! [X0] :
( pred_attacker(tuple_R_in_2(X0,constr_h(constr_xor(constr_xor(name_r0x30,X0),name_k))))
=> pred_attacker(tuple_R_out_4(name_objective_R)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax106) ).
fof(f108,conjecture,
pred_attacker(name_objective_R),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co0) ).
fof(f109,negated_conjecture,
~ pred_attacker(name_objective_R),
inference(negated_conjecture,[status(cth)],[f108]) ).
fof(f110,plain,
~ pred_attacker(name_objective_R),
inference(flattening,[],[f109]) ).
fof(f112,plain,
! [X0,X1] :
( pred_attacker(constr_xor(X0,X1))
| ~ pred_attacker(X0)
| ~ pred_attacker(X1) ),
inference(ennf_transformation,[],[f71]) ).
fof(f113,plain,
! [X0,X1] :
( pred_attacker(constr_xor(X0,X1))
| ~ pred_attacker(X0)
| ~ pred_attacker(X1) ),
inference(flattening,[],[f112]) ).
fof(f118,plain,
! [X0,X1] :
( pred_attacker(X0)
| ~ pred_attacker(tuple_knowledge_from_1st_round_out_2(X0,X1)) ),
inference(ennf_transformation,[],[f76]) ).
fof(f119,plain,
! [X0,X1] :
( pred_attacker(X1)
| ~ pred_attacker(tuple_knowledge_from_1st_round_out_2(X0,X1)) ),
inference(ennf_transformation,[],[f77]) ).
fof(f121,plain,
! [X0] :
( pred_attacker(X0)
| ~ pred_attacker(tuple_knowledge_from_1st_round_out_1(X0)) ),
inference(ennf_transformation,[],[f79]) ).
fof(f124,plain,
! [X0] :
( pred_attacker(X0)
| ~ pred_attacker(tuple_R_out_4(X0)) ),
inference(ennf_transformation,[],[f84]) ).
fof(f128,plain,
! [X0] :
( pred_attacker(X0)
| ~ pred_attacker(tuple_R_out_1(X0)) ),
inference(ennf_transformation,[],[f88]) ).
fof(f129,plain,
! [X0,X1] :
( pred_attacker(tuple_R_in_2(X0,X1))
| ~ pred_attacker(X0)
| ~ pred_attacker(X1) ),
inference(ennf_transformation,[],[f89]) ).
fof(f130,plain,
! [X0,X1] :
( pred_attacker(tuple_R_in_2(X0,X1))
| ~ pred_attacker(X0)
| ~ pred_attacker(X1) ),
inference(flattening,[],[f129]) ).
fof(f138,plain,
! [X0] :
( pred_attacker(tuple_R_out_4(name_objective_R))
| ~ pred_attacker(tuple_R_in_2(X0,constr_h(constr_xor(constr_xor(name_r0x30,X0),name_k)))) ),
inference(ennf_transformation,[],[f107]) ).
fof(f205,plain,
! [X0] : constr_ZERO = constr_xor(X0,X0),
inference(cnf_transformation,[],[f67]) ).
fof(f206,plain,
! [X0] : constr_xor(X0,constr_ZERO) = X0,
inference(cnf_transformation,[],[f68]) ).
fof(f207,plain,
! [X0,X1] : constr_xor(X0,X1) = constr_xor(X1,X0),
inference(cnf_transformation,[],[f69]) ).
fof(f208,plain,
! [X2,X0,X1] : constr_xor(X0,constr_xor(X1,X2)) = constr_xor(constr_xor(X0,X1),X2),
inference(cnf_transformation,[],[f70]) ).
fof(f209,plain,
! [X0,X1] :
( pred_attacker(constr_xor(X0,X1))
| ~ pred_attacker(X0)
| ~ pred_attacker(X1) ),
inference(cnf_transformation,[],[f113]) ).
fof(f214,plain,
! [X0,X1] :
( ~ pred_attacker(tuple_knowledge_from_1st_round_out_2(X0,X1))
| pred_attacker(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f215,plain,
! [X0,X1] :
( ~ pred_attacker(tuple_knowledge_from_1st_round_out_2(X0,X1))
| pred_attacker(X1) ),
inference(cnf_transformation,[],[f119]) ).
fof(f217,plain,
! [X0] :
( ~ pred_attacker(tuple_knowledge_from_1st_round_out_1(X0))
| pred_attacker(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f222,plain,
! [X0] :
( ~ pred_attacker(tuple_R_out_4(X0))
| pred_attacker(X0) ),
inference(cnf_transformation,[],[f124]) ).
fof(f226,plain,
! [X0] :
( ~ pred_attacker(tuple_R_out_1(X0))
| pred_attacker(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f227,plain,
! [X0,X1] :
( pred_attacker(tuple_R_in_2(X0,X1))
| ~ pred_attacker(X0)
| ~ pred_attacker(X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f239,plain,
pred_attacker(tuple_knowledge_from_1st_round_out_1(name_r0x30_from_1st)),
inference(cnf_transformation,[],[f102]) ).
fof(f240,plain,
pred_attacker(tuple_knowledge_from_1st_round_out_2(name_r1_from_1st,constr_h(constr_xor(constr_xor(name_r0x30_from_1st,name_r1_from_1st),name_k)))),
inference(cnf_transformation,[],[f103]) ).
fof(f242,plain,
pred_attacker(tuple_R_out_1(name_r0x30)),
inference(cnf_transformation,[],[f105]) ).
fof(f244,plain,
! [X0] :
( pred_attacker(tuple_R_out_4(name_objective_R))
| ~ pred_attacker(tuple_R_in_2(X0,constr_h(constr_xor(constr_xor(name_r0x30,X0),name_k)))) ),
inference(cnf_transformation,[],[f138]) ).
fof(f245,plain,
~ pred_attacker(name_objective_R),
inference(cnf_transformation,[],[f110]) ).
fof(f247,definition,
( spl0_1
<=> ! [X0] : ~ pred_attacker(tuple_R_in_2(X0,constr_h(constr_xor(constr_xor(name_r0x30,X0),name_k)))) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f248,plain,
( ! [X0] : ~ pred_attacker(tuple_R_in_2(X0,constr_h(constr_xor(constr_xor(name_r0x30,X0),name_k))))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f247]) ).
fof(f250,definition,
( spl0_2
<=> pred_attacker(tuple_R_out_4(name_objective_R)) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f252,plain,
( pred_attacker(tuple_R_out_4(name_objective_R))
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f250]) ).
fof(f253,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f244,f250,f247]) ).
fof(f255,plain,
pred_attacker(name_r0x30_from_1st),
inference(resolution,[],[f217,f239]) ).
fof(f257,plain,
( pred_attacker(name_objective_R)
| ~ spl0_2 ),
inference(resolution,[],[f222,f252]) ).
fof(f259,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f257,f245]) ).
fof(f260,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f259]) ).
fof(f263,plain,
pred_attacker(name_r0x30),
inference(resolution,[],[f226,f242]) ).
fof(f271,plain,
pred_attacker(constr_h(constr_xor(constr_xor(name_r0x30_from_1st,name_r1_from_1st),name_k))),
inference(resolution,[],[f240,f215]) ).
fof(f272,plain,
pred_attacker(name_r1_from_1st),
inference(resolution,[],[f240,f214]) ).
fof(f273,plain,
( ! [X0] :
( ~ pred_attacker(X0)
| ~ pred_attacker(constr_h(constr_xor(constr_xor(name_r0x30,X0),name_k))) )
| ~ spl0_1 ),
inference(resolution,[],[f248,f227]) ).
fof(f280,plain,
! [X0] : constr_xor(constr_ZERO,X0) = X0,
inference(superposition,[],[f207,f206]) ).
fof(f312,plain,
pred_attacker(constr_h(constr_xor(name_k,constr_xor(name_r0x30_from_1st,name_r1_from_1st)))),
inference(forward_demodulation,[],[f271,f207]) ).
fof(f318,plain,
( ! [X0] :
( ~ pred_attacker(constr_h(constr_xor(name_k,constr_xor(name_r0x30,X0))))
| ~ pred_attacker(X0) )
| ~ spl0_1 ),
inference(forward_demodulation,[],[f273,f207]) ).
fof(f328,plain,
! [X0,X1] : constr_xor(X0,constr_xor(X0,X1)) = constr_xor(constr_ZERO,X1),
inference(superposition,[],[f208,f205]) ).
fof(f351,plain,
! [X0,X1] : constr_xor(X0,constr_xor(X0,X1)) = X1,
inference(forward_demodulation,[],[f328,f280]) ).
fof(f377,plain,
( ! [X0] :
( ~ pred_attacker(constr_xor(name_r0x30,X0))
| ~ pred_attacker(constr_h(constr_xor(name_k,X0))) )
| ~ spl0_1 ),
inference(superposition,[],[f318,f351]) ).
fof(f826,plain,
( ! [X0] :
( ~ pred_attacker(constr_h(constr_xor(name_k,X0)))
| ~ pred_attacker(name_r0x30)
| ~ pred_attacker(X0) )
| ~ spl0_1 ),
inference(resolution,[],[f377,f209]) ).
fof(f836,plain,
( ! [X0] :
( ~ pred_attacker(constr_h(constr_xor(name_k,X0)))
| ~ pred_attacker(X0) )
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f826,f263]) ).
fof(f842,plain,
( ~ pred_attacker(constr_xor(name_r0x30_from_1st,name_r1_from_1st))
| ~ spl0_1 ),
inference(resolution,[],[f836,f312]) ).
fof(f852,plain,
( ~ pred_attacker(name_r0x30_from_1st)
| ~ pred_attacker(name_r1_from_1st)
| ~ spl0_1 ),
inference(resolution,[],[f842,f209]) ).
fof(f853,plain,
( ~ pred_attacker(name_r1_from_1st)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f852,f255]) ).
fof(f854,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f853,f272]) ).
fof(f855,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f854]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f253]) ).
cnf(s2,plain,
~ spl0_2,
inference(sat_conversion,[],[f260]) ).
cnf(s3,plain,
~ spl0_1,
inference(sat_conversion,[],[f855]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s2,s3]) ).
fof(f856,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW948+1 : TPTP v9.3.1. Released v7.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n018.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Mon Sep 28 14:49:40 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running first-order theorem proving
% 0.08/0.21 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
% 3.10/1.10 % (3444186)Detected formulas, will run a generic FOF schedule.
% 3.10/1.10 % (3444191)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=158890913:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.10/1.10 % (3444195)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2642570571:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.10/1.10 % (3444192)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=2615552933:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.10/1.10 % (3444197)dis-21_1_sil=8000:lcm=predicate:random_seed=1356679309: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)
% 3.10/1.10 % (3444196)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1604296657:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.10/1.10 % (3444193)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=1132686240:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.10/1.10 % (3444194)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3268419448:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.10/1.10 % (3444194)Refutation not found, incomplete strategy
% 3.10/1.10 % (3444194)------------------------------
% 3.10/1.10 % (3444194)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.10 % (3444194)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.10 % (3444194)CaDiCaL version: 2.1.3
% 3.10/1.10 % (3444194)Termination reason: Refutation not found, incomplete strategy
% 3.10/1.10 % (3444194)Time elapsed: 0.001 s
% 3.10/1.10 % (3444194)Peak memory usage: 87 MB
% 3.10/1.10 % (3444195)Refutation not found, incomplete strategy
% 3.10/1.10 % (3444195)------------------------------
% 3.10/1.10 % (3444195)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.10 % (3444195)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.10 % (3444195)CaDiCaL version: 2.1.3
% 3.10/1.10 % (3444195)Termination reason: Refutation not found, incomplete strategy
% 3.10/1.10 % (3444195)Time elapsed: 0.001 s
% 3.10/1.10 % (3444195)Peak memory usage: 87 MB
% 3.10/1.10 % (3444197)Refutation not found, incomplete strategy
% 3.10/1.10 % (3444197)------------------------------
% 3.10/1.10 % (3444197)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.10/1.10 % (3444197)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.10/1.10 % (3444197)CaDiCaL version: 2.1.3
% 3.10/1.10 % (3444197)Termination reason: Refutation not found, incomplete strategy
% 3.10/1.10 % (3444197)Time elapsed: 0.004 s
% 3.10/1.10 % (3444197)Peak memory usage: 88 MB
% 3.10/1.10 % (3444197)Instructions burned: 5 (million)
% 3.10/1.10 % (3444196)First to succeed.
% 3.10/1.10 % (3444196)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3444186"
% 3.10/1.10 % (3444197)------------------------------
% 3.10/1.10 % (3444197)------------------------------
% 3.10/1.10 % (3444195)------------------------------
% 3.10/1.10 % (3444195)------------------------------
% 3.10/1.10 % (3444194)------------------------------
% 3.10/1.10 % (3444194)------------------------------
% 3.10/1.10 % (3444196)Refutation found. Thanks to Tanya!
% 3.10/1.10 % SZS status Theorem for theBenchmark
% 3.10/1.10 % SZS output start Proof for theBenchmark
% See solution above
% 3.68/1.29 % (3444196)------------------------------
% 3.68/1.29 % (3444196)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.68/1.29 % (3444196)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.68/1.29 % (3444196)CaDiCaL version: 2.1.3
% 3.68/1.29 % (3444196)Termination reason: Refutation
% 3.68/1.29 % (3444196)Time elapsed: 0.018 s
% 3.68/1.29 % (3444196)Peak memory usage: 90 MB
% 3.68/1.29 % (3444196)Instructions burned: 25 (million)
% 3.68/1.29 % (3444196)------------------------------
% 3.68/1.29 % (3444196)------------------------------
% 3.68/1.29 % (3444186)Success in time 0.442 s
% 3.68/1.29 % Vampire exiting
%------------------------------------------------------------------------------