%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV236+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 09:07:05 AM UTC 2026
% Result : Theorem 21.03s 3.18s
% Output : CNFRefutation 21.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 36 ( 26 unt; 0 def)
% Number of atoms : 50 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 25 ( 11 ~; 8 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 11 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(xor_commutative,axiom,
! [X1,X2] : xor(X1,X2) = xor(X2,X1),
file('theBenchmark.p',xor_commutative) ).
fof(xor_associative,axiom,
! [X1,X2,X3] : xor(X1,xor(X2,X3)) = xor(xor(X1,X2),X3),
file('theBenchmark.p',xor_associative) ).
fof(xor_rules_1,axiom,
! [X1] : xor(X1,id) = X1,
file('theBenchmark.p',xor_rules_1) ).
fof(xor_rules_2,axiom,
! [X1] : xor(X1,X1) = id,
file('theBenchmark.p',xor_rules_2) ).
fof(key_part_import___part_1,axiom,
! [Xk,Xtype] :
( ( p(Xtype)
& p(Xk) )
=> p(crypt(xor(km,xor(kp,Xtype)),Xk)) ),
file('theBenchmark.p',key_part_import___part_1) ).
fof(combine_with_XOR,axiom,
! [X1,X2] :
( ( p(X2)
& p(X1) )
=> p(xor(X1,X2)) ),
file('theBenchmark.p',combine_with_XOR) ).
fof(find_known_exporter,conjecture,
? [X] :
( p(X)
& p(crypt(xor(km,exp),X)) ),
file('theBenchmark.p',find_known_exporter) ).
fof(find_known_exporter_neg,negated_conjecture,
~ ? [X] :
( p(X)
& p(crypt(xor(km,exp),X)) ),
inference(assume_negation,[status(cth)],[find_known_exporter]) ).
cnf(c_19,plain,
xor(A,B) = xor(B,A),
inference(clausify,[status(thm)],[xor_commutative]) ).
cnf(c_20,plain,
xor(xor(A,B),C) = xor(A,xor(B,C)),
inference(clausify,[status(thm)],[xor_associative]) ).
cnf(c_22,plain,
xor(A,id) = A,
inference(clausify,[status(thm)],[xor_rules_1]) ).
cnf(c_23,plain,
xor(A,A) = id,
inference(clausify,[status(thm)],[xor_rules_2]) ).
cnf(c_26,plain,
( p(crypt(xor(km,xor(kp,B)),A))
| ~ p(B)
| ~ p(A) ),
inference(clausify,[status(thm)],[key_part_import___part_1]) ).
cnf(c_32,plain,
( p(xor(A,B))
| ~ p(B)
| ~ p(A) ),
inference(clausify,[status(thm)],[combine_with_XOR]) ).
fof(initial_knowledge_of_intruder_1,axiom,
p(kp),
file('theBenchmark.p',initial_knowledge_of_intruder_1) ).
cnf(c_36,plain,
p(kp),
inference(clausify,[status(thm)],[initial_knowledge_of_intruder_1]) ).
fof(initial_knowledge_of_intruder_2,axiom,
p(imp),
file('theBenchmark.p',initial_knowledge_of_intruder_2) ).
cnf(c_37,plain,
p(imp),
inference(clausify,[status(thm)],[initial_knowledge_of_intruder_2]) ).
fof(initial_knowledge_of_intruder_9,axiom,
p(exp),
file('theBenchmark.p',initial_knowledge_of_intruder_9) ).
cnf(c_44,plain,
p(exp),
inference(clausify,[status(thm)],[initial_knowledge_of_intruder_9]) ).
cnf(c_46,negated_conjecture,
( ~ p(A)
| ~ p(crypt(xor(km,exp),A)) ),
inference(clausify,[status(thm)],[find_known_exporter_neg]) ).
cnf(c_15933,plain,
A = xor(id,A),
inference(paramod,[status(thm)],[c_22,c_19]) ).
cnf(c_49,plain,
xor(id,A) = A,
inference(copy,[status(thm)],[c_15933]) ).
cnf(c_15934,plain,
xor(id,A) = xor(B,xor(B,A)),
inference(paramod,[status(thm)],[c_23,c_20]) ).
cnf(c_15935,plain,
A = xor(B,xor(B,A)),
inference(paramod,[status(thm)],[c_49,c_15934]) ).
cnf(c_50,plain,
xor(A,xor(A,B)) = B,
inference(copy,[status(thm)],[c_15935]) ).
cnf(c_15936,plain,
( p(xor(imp,A))
| ~ p(A) ),
inference(resolve,[status(thm)],[c_32,c_37]) ).
cnf(c_15937,plain,
p(xor(imp,exp)),
inference(resolve,[status(thm)],[c_15936,c_44]) ).
cnf(c_257,plain,
p(xor(exp,imp)),
inference(paramod,[status(thm)],[c_19,c_15937]) ).
cnf(c_15938,plain,
( p(xor(kp,A))
| ~ p(A) ),
inference(resolve,[status(thm)],[c_32,c_36]) ).
cnf(c_258,plain,
p(xor(kp,exp)),
inference(resolve,[status(thm)],[c_15938,c_44]) ).
cnf(c_15745,negated_conjecture,
~ p(crypt(xor(km,exp),xor(exp,imp))),
inference(resolve,[status(thm)],[c_46,c_257]) ).
cnf(c_15939,plain,
( p(crypt(xor(km,xor(kp,A)),xor(exp,imp)))
| ~ p(A) ),
inference(resolve,[status(thm)],[c_26,c_257]) ).
cnf(c_15940,plain,
p(crypt(xor(km,xor(kp,xor(kp,exp))),xor(exp,imp))),
inference(resolve,[status(thm)],[c_15939,c_258]) ).
cnf(c_15941,plain,
p(crypt(xor(km,exp),xor(exp,imp))),
inference(paramod,[status(thm)],[c_50,c_15940]) ).
cnf(c_15932,plain,
$false,
inference(resolve,[status(thm)],[c_15745,c_15941]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV236+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n008.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 13:21:54 UTC 2026
% 0.18/0.44 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 3763919 was started by sandbox on n008,
% 0.18/0.45 % Sat Sep 26 13:21:54 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 21.03/3.18
% 21.03/3.18 % SZS status Theorem for theBenchmark
% 21.03/3.18
% 21.03/3.18 % Proof 1 at 2.18 (+ 0.50) seconds.
% 21.03/3.18 % Length of proof is 23.
% 21.03/3.18 % Level of proof is 4.
% 21.03/3.18 % Maximum clause weight is 37.000.
% 21.03/3.18 % Given clauses 167.
% 21.03/3.18
% 21.03/3.18 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------