%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV234+2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n017.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 01:08:27 PM UTC 2026
% Result : Theorem 3.94s 1.24s
% Output : Refutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 57 ( 35 unt; 0 def)
% Number of atoms : 105 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 94 ( 46 ~; 43 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-2 aty)
% Number of variables : 87 ( 87 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [X0,X1] :
( ( public(X0)
& public(X1) )
=> public(enc(enc(inv(xor(data,km)),X0),X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_data_cmd) ).
fof(f6,axiom,
! [X0,X1,X2] :
( ( public(X1)
& public(enc(xor(X0,X1),X2))
& public(enc(xor(km,imp),X0)) )
=> public(enc(xor(km,X1),X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',key_import_cmd) ).
fof(f8,axiom,
! [X0,X1,X2] : enc(X0,enc(inv(X0),X1)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',encrypt_decrypt_cancel) ).
fof(f9,axiom,
! [X0,X1,X2] : xor(X0,X1) = xor(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_commutes) ).
fof(f10,axiom,
! [X0,X1,X2] : xor(X0,xor(X1,X2)) = xor(xor(X0,X1),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_assosciative) ).
fof(f11,axiom,
! [X0,X1,X2] : xor(X0,X0) = z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_self_cancel) ).
fof(f12,axiom,
! [X0,X1,X2] : xor(X0,z) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xor_zero) ).
fof(f14,axiom,
public(data),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge2) ).
fof(f17,axiom,
public(enc(xor(kek,pin),pp)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge5) ).
fof(f20,axiom,
public(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge8) ).
fof(f21,axiom,
public(enc(xor(km,imp),xor(kek,xor(pin,data)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',initial_knowledge9) ).
fof(f22,conjecture,
public(enc(pp,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f23,negated_conjecture,
~ public(enc(pp,a)),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f24,plain,
! [X0,X1] : enc(X0,enc(inv(X0),X1)) = X1,
inference(rectify,[],[f8]) ).
fof(f25,plain,
! [X0,X1] : xor(X0,X1) = xor(X1,X0),
inference(rectify,[],[f9]) ).
fof(f26,plain,
! [X0] : xor(X0,X0) = z,
inference(rectify,[],[f11]) ).
fof(f27,plain,
! [X0] : xor(X0,z) = X0,
inference(rectify,[],[f12]) ).
fof(f28,plain,
~ public(enc(pp,a)),
inference(flattening,[],[f23]) ).
fof(f36,plain,
! [X0,X1] :
( public(enc(enc(inv(xor(data,km)),X0),X1))
| ~ public(X0)
| ~ public(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f37,plain,
! [X0,X1] :
( public(enc(enc(inv(xor(data,km)),X0),X1))
| ~ public(X0)
| ~ public(X1) ),
inference(flattening,[],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( public(enc(xor(km,X1),X2))
| ~ public(X1)
| ~ public(enc(xor(X0,X1),X2))
| ~ public(enc(xor(km,imp),X0)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f39,plain,
! [X0,X1,X2] :
( public(enc(xor(km,X1),X2))
| ~ public(X1)
| ~ public(enc(xor(X0,X1),X2))
| ~ public(enc(xor(km,imp),X0)) ),
inference(flattening,[],[f38]) ).
fof(f46,plain,
! [X0,X1] :
( public(enc(enc(inv(xor(data,km)),X0),X1))
| ~ public(X0)
| ~ public(X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f47,plain,
! [X2,X0,X1] :
( ~ public(enc(xor(km,imp),X0))
| ~ public(X1)
| ~ public(enc(xor(X0,X1),X2))
| public(enc(xor(km,X1),X2)) ),
inference(cnf_transformation,[],[f39]) ).
fof(f49,plain,
! [X0,X1] : enc(X0,enc(inv(X0),X1)) = X1,
inference(cnf_transformation,[],[f24]) ).
fof(f50,plain,
! [X0,X1] : xor(X0,X1) = xor(X1,X0),
inference(cnf_transformation,[],[f25]) ).
fof(f51,plain,
! [X2,X0,X1] : xor(X0,xor(X1,X2)) = xor(xor(X0,X1),X2),
inference(cnf_transformation,[],[f10]) ).
fof(f52,plain,
! [X0] : xor(X0,X0) = z,
inference(cnf_transformation,[],[f26]) ).
fof(f53,plain,
! [X0] : xor(X0,z) = X0,
inference(cnf_transformation,[],[f27]) ).
fof(f55,plain,
public(data),
inference(cnf_transformation,[],[f14]) ).
fof(f58,plain,
public(enc(xor(kek,pin),pp)),
inference(cnf_transformation,[],[f17]) ).
fof(f61,plain,
public(a),
inference(cnf_transformation,[],[f20]) ).
fof(f62,plain,
public(enc(xor(km,imp),xor(kek,xor(pin,data)))),
inference(cnf_transformation,[],[f21]) ).
fof(f63,plain,
~ public(enc(pp,a)),
inference(cnf_transformation,[],[f28]) ).
fof(f67,plain,
! [X0] : xor(z,X0) = X0,
inference(superposition,[],[f50,f53]) ).
fof(f71,plain,
public(enc(xor(pin,kek),pp)),
inference(superposition,[],[f58,f50]) ).
fof(f77,plain,
! [X0,X1] : enc(inv(inv(X1)),X0) = enc(X1,X0),
inference(superposition,[],[f49,f49]) ).
fof(f85,plain,
public(enc(xor(km,imp),xor(kek,xor(data,pin)))),
inference(forward_demodulation,[],[f62,f50]) ).
fof(f86,plain,
! [X0,X1] :
( public(enc(enc(inv(xor(km,data)),X0),X1))
| ~ public(X0)
| ~ public(X1) ),
inference(forward_demodulation,[],[f46,f50]) ).
fof(f87,plain,
! [X0,X1] :
( public(enc(X0,X1))
| ~ public(enc(inv(inv(xor(km,data))),X0))
| ~ public(X1) ),
inference(superposition,[],[f86,f49]) ).
fof(f96,plain,
! [X0,X1] :
( ~ public(X0)
| ~ public(enc(xor(xor(kek,xor(data,pin)),X0),X1))
| public(enc(xor(km,X0),X1)) ),
inference(resolution,[],[f47,f85]) ).
fof(f136,plain,
! [X0,X1] : xor(X0,xor(X0,X1)) = xor(z,X1),
inference(superposition,[],[f51,f52]) ).
fof(f144,plain,
! [X2,X0,X1] : xor(X0,xor(X1,X2)) = xor(X1,xor(X2,X0)),
inference(superposition,[],[f51,f50]) ).
fof(f152,plain,
! [X0,X1] : xor(X0,xor(X0,X1)) = X1,
inference(forward_demodulation,[],[f136,f67]) ).
fof(f163,plain,
! [X0,X1] :
( ~ public(enc(xor(km,data),X0))
| public(enc(X0,X1))
| ~ public(X1) ),
inference(forward_demodulation,[],[f87,f77]) ).
fof(f181,plain,
! [X0,X1] :
( ~ public(enc(xor(kek,xor(xor(data,pin),X0)),X1))
| ~ public(X0)
| public(enc(xor(km,X0),X1)) ),
inference(forward_demodulation,[],[f96,f51]) ).
fof(f182,plain,
! [X0,X1] :
( public(enc(xor(km,X0),X1))
| ~ public(X0)
| ~ public(enc(xor(kek,xor(data,xor(pin,X0))),X1)) ),
inference(forward_demodulation,[],[f181,f51]) ).
fof(f190,plain,
! [X0,X1] :
( ~ public(data)
| ~ public(enc(xor(kek,xor(data,xor(pin,data))),X0))
| public(enc(X0,X1))
| ~ public(X1) ),
inference(resolution,[],[f182,f163]) ).
fof(f199,plain,
! [X0,X1] :
( ~ public(enc(xor(kek,xor(data,xor(pin,data))),X0))
| public(enc(X0,X1))
| ~ public(X1) ),
inference(forward_subsumption_resolution,[],[f190,f55]) ).
fof(f202,plain,
! [X0,X1] :
( ~ public(enc(xor(kek,xor(data,xor(data,pin))),X0))
| public(enc(X0,X1))
| ~ public(X1) ),
inference(forward_demodulation,[],[f199,f50]) ).
fof(f782,plain,
! [X0,X1] :
( ~ public(enc(xor(data,xor(xor(data,pin),kek)),X0))
| public(enc(X0,X1))
| ~ public(X1) ),
inference(forward_demodulation,[],[f202,f144]) ).
fof(f783,plain,
! [X0,X1] :
( ~ public(enc(xor(data,xor(kek,xor(data,pin))),X0))
| public(enc(X0,X1))
| ~ public(X1) ),
inference(forward_demodulation,[],[f782,f50]) ).
fof(f784,plain,
! [X0,X1] :
( ~ public(enc(xor(data,xor(data,xor(pin,kek))),X0))
| public(enc(X0,X1))
| ~ public(X1) ),
inference(forward_demodulation,[],[f783,f144]) ).
fof(f785,plain,
! [X0,X1] :
( ~ public(enc(xor(pin,kek),X0))
| public(enc(X0,X1))
| ~ public(X1) ),
inference(forward_demodulation,[],[f784,f152]) ).
fof(f802,plain,
! [X0] :
( ~ public(X0)
| public(enc(pp,X0)) ),
inference(resolution,[],[f785,f71]) ).
fof(f1623,plain,
public(enc(pp,a)),
inference(resolution,[],[f802,f61]) ).
fof(f1624,plain,
$false,
inference(forward_subsumption_resolution,[],[f1623,f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV234+2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.20 % Computer : n017.cluster.edu
% 0.07/0.20 % Model : x86_64 x86_64
% 0.07/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.20 % Memory : 8046.5625MB
% 0.07/0.20 % OS : Linux 6.8.0-71-generic
% 0.07/0.20 % CPULimit : 300
% 0.07/0.20 % WCLimit : 300
% 0.07/0.20 % DateTime : Mon Sep 28 10:10:21 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.22 Running first-order theorem proving
% 0.07/0.22 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
% 3.94/1.24 % (3450417)Detected formulas, will run a generic FOF schedule.
% 3.94/1.24 % (3450422)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=3010175441:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.94/1.24 % (3450423)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=352847221:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.94/1.24 % (3450426)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1965695520:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.94/1.24 % (3450428)dis-21_1_sil=8000:lcm=predicate:random_seed=2463854620: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)
% 3.94/1.24 % (3450425)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4163535396:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.94/1.24 % (3450424)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=1839164127:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.94/1.24 % (3450425)Refutation not found, incomplete strategy
% 3.94/1.24 % (3450425)------------------------------
% 3.94/1.24 % (3450425)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.24 % (3450425)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.24 % (3450425)CaDiCaL version: 2.1.3
% 3.94/1.24 % (3450425)Termination reason: Refutation not found, incomplete strategy
% 3.94/1.24 % (3450425)Time elapsed: 0.001 s
% 3.94/1.24 % (3450425)Peak memory usage: 88 MB
% 3.94/1.24 % (3450428)Refutation not found, incomplete strategy
% 3.94/1.24 % (3450428)------------------------------
% 3.94/1.24 % (3450428)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.24 % (3450428)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.24 % (3450428)CaDiCaL version: 2.1.3
% 3.94/1.24 % (3450428)Termination reason: Refutation not found, incomplete strategy
% 3.94/1.24 % (3450428)Time elapsed: 0.002 s
% 3.94/1.24 % (3450428)Peak memory usage: 88 MB
% 3.94/1.24 % (3450428)Instructions burned: 1 (million)
% 3.94/1.24 % (3450427)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=4138328219:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.94/1.24 % (3450426)Instruction limit reached!
% 3.94/1.24 % (3450426)------------------------------
% 3.94/1.24 % (3450426)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.24 % (3450426)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.24 % (3450426)CaDiCaL version: 2.1.3
% 3.94/1.24 % (3450426)Termination reason: Instruction limit
% 3.94/1.24 % (3450426)Termination phase: Saturation
% 3.94/1.24 % (3450426)Time elapsed: 0.058 s
% 3.94/1.24 % (3450426)Peak memory usage: 88 MB
% 3.94/1.24 % (3450426)Instructions burned: 121 (million)
% 3.94/1.24 % (3450427)First to succeed.
% 3.94/1.24 % (3450427)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3450417"
% 3.94/1.24 % (3450436)lrs+10_1_sil=8000:sp=occurrence:random_seed=3176304180:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.94/1.24 % (3450436)Refutation not found, incomplete strategy
% 3.94/1.24 % (3450436)------------------------------
% 3.94/1.24 % (3450436)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.24 % (3450436)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.24 % (3450436)CaDiCaL version: 2.1.3
% 3.94/1.24 % (3450436)Termination reason: Refutation not found, incomplete strategy
% 3.94/1.24 % (3450436)Time elapsed: 0.004 s
% 3.94/1.24 % (3450436)Peak memory usage: 88 MB
% 3.94/1.24 % (3450436)Instructions burned: 3 (million)
% 3.94/1.24 % (3450428)------------------------------
% 3.94/1.24 % (3450428)------------------------------
% 3.94/1.24 % (3450425)------------------------------
% 3.94/1.24 % (3450425)------------------------------
% 3.94/1.24 % (3450427)Refutation found. Thanks to Tanya!
% 3.94/1.24 % SZS status Theorem for theBenchmark
% 3.94/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 3.94/1.24 % (3450427)------------------------------
% 3.94/1.24 % (3450427)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.94/1.24 % (3450427)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.94/1.24 % (3450427)CaDiCaL version: 2.1.3
% 3.94/1.24 % (3450427)Termination reason: Refutation
% 3.94/1.24 % (3450427)Time elapsed: 0.057 s
% 3.94/1.24 % (3450427)Peak memory usage: 89 MB
% 3.94/1.24 % (3450427)Instructions burned: 81 (million)
% 3.94/1.24 % (3450427)------------------------------
% 3.94/1.24 % (3450427)------------------------------
% 3.94/1.24 % (3450417)Success in time 0.483 s
% 3.94/1.24 % Vampire exiting
%------------------------------------------------------------------------------