%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV237+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 : Sun Sep 27 09:07:06 AM UTC 2026
% Result : Theorem 18.85s 2.75s
% Output : CNFRefutation 18.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 22 ( 14 unt; 0 def)
% Number of atoms : 40 ( 2 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 14 ~; 12 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 22 ( 4 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(enc_dec_cancel,axiom,
! [U,V] : enc(i(U),enc(U,V)) = V,
file('theBenchmark.p',enc_dec_cancel) ).
fof(encrypt_a_stored_comms_key,axiom,
! [U,V,W] :
( ( p(W)
& p(V)
& p(U) )
=> p(enc(enc(i(tmk),V),enc(i(tc),U))) ),
file('theBenchmark.p',encrypt_a_stored_comms_key) ).
fof(encrypt_clear_key_as_Tcomms_key,axiom,
! [U,V,W] :
( ( p(W)
& p(V)
& p(U) )
=> p(enc(tc,U)) ),
file('theBenchmark.p',encrypt_clear_key_as_Tcomms_key) ).
fof(co1,conjecture,
p(enc(pp,a)),
file('theBenchmark.p',co1) ).
fof(co1_neg,negated_conjecture,
~ p(enc(pp,a)),
inference(assume_negation,[status(cth)],[co1]) ).
cnf(c_18,plain,
enc(i(A),enc(A,B)) = B,
inference(clausify,[status(thm)],[enc_dec_cancel]) ).
cnf(c_26,plain,
( p(enc(enc(i(tmk),B),enc(i(tc),A)))
| ~ p(C)
| ~ p(B)
| ~ p(A) ),
inference(clausify,[status(thm)],[encrypt_a_stored_comms_key]) ).
cnf(c_27,plain,
( p(enc(tc,A))
| ~ p(C)
| ~ p(B)
| ~ p(A) ),
inference(clausify,[status(thm)],[encrypt_clear_key_as_Tcomms_key]) ).
fof(intruder_knows_1,axiom,
p(enc(tmk,pp)),
file('theBenchmark.p',intruder_knows_1) ).
cnf(c_34,plain,
p(enc(tmk,pp)),
inference(clausify,[status(thm)],[intruder_knows_1]) ).
fof(intruder_knows_8,axiom,
p(a),
file('theBenchmark.p',intruder_knows_8) ).
cnf(c_41,plain,
p(a),
inference(clausify,[status(thm)],[intruder_knows_8]) ).
cnf(c_42,negated_conjecture,
~ p(enc(pp,a)),
inference(clausify,[status(thm)],[co1_neg]) ).
cnf(c_51,plain,
( p(enc(enc(i(tmk),B),enc(i(tc),A)))
| ~ p(B)
| ~ p(A) ),
inference(factor,[status(thm)],[c_26]) ).
cnf(c_52,plain,
( p(enc(tc,A))
| ~ p(B)
| ~ p(A) ),
inference(factor,[status(thm)],[c_27]) ).
cnf(c_71,plain,
( p(enc(tc,A))
| ~ p(A) ),
inference(factor,[status(thm)],[c_52]) ).
cnf(c_1564,plain,
p(enc(tc,a)),
inference(resolve,[status(thm)],[c_71,c_41]) ).
cnf(c_18220,plain,
( p(enc(enc(i(tmk),A),enc(i(tc),enc(tc,a))))
| ~ p(A) ),
inference(resolve,[status(thm)],[c_51,c_1564]) ).
cnf(c_18221,plain,
p(enc(enc(i(tmk),enc(tmk,pp)),enc(i(tc),enc(tc,a)))),
inference(resolve,[status(thm)],[c_18220,c_34]) ).
cnf(c_18222,plain,
p(enc(pp,enc(i(tc),enc(tc,a)))),
inference(paramod,[status(thm)],[c_18,c_18221]) ).
cnf(c_18223,plain,
p(enc(pp,a)),
inference(paramod,[status(thm)],[c_18,c_18222]) ).
cnf(c_18219,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_42,c_18223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV237+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.31 % CPULimit : 300
% 0.03/0.31 % WCLimit : 300
% 0.03/0.31 % DateTime : Sat Sep 26 13:20:51 UTC 2026
% 0.03/0.31 % CPUTime :
% 0.03/0.31 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.31 % Process 702814 was started by sandbox2 on n012,
% 0.03/0.31 % Sat Sep 26 13:20:51 2026
% 0.03/0.31 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/0.32
% 0.03/0.32 % From the command line: assign(max_seconds, 300).
% 18.85/2.75
% 18.85/2.75 % Assigning unary symbol i kb_weight 0 and highest precedence (16).
% 18.85/2.75
% 18.85/2.75 % SZS status Theorem for theBenchmark
% 18.85/2.75
% 18.85/2.75 % Proof 1 at 1.73 (+ 0.49) seconds.
% 18.85/2.75 % Length of proof is 15.
% 18.85/2.75 % Level of proof is 5.
% 18.85/2.75 % Maximum clause weight is 40.000.
% 18.85/2.75 % Given clauses 54.
% 18.85/2.75
% 18.85/2.75 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------