%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV234+2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n020.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 : Thu Sep 24 02:46:57 PM UTC 2026
% Result : Theorem 7.17s 1.51s
% Output : CNFRefutation 7.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 46 ( 29 unt; 0 def)
% Number of atoms : 87 ( 16 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 80 ( 39 ~; 36 |; 3 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 74 ( 74 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [U,V] :
( ( public(V)
& public(U) )
=> public(enc(enc(inv(xor(data,km)),U),V)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [U,V,W] :
( ( public(enc(xor(km,imp),U))
& public(enc(xor(U,V),W))
& public(V) )
=> public(enc(xor(km,V),W)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U,V,W] : enc(U,enc(inv(U),V)) = V,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [U,V,W] : xor(U,V) = xor(V,U),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [U,V,W] : xor(U,xor(V,W)) = xor(xor(U,V),W),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [U,V,W] : xor(U,U) = z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [U,V,W] : xor(U,z) = U,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
public(data),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
public(enc(xor(kek,pin),pp)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
public(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
public(enc(xor(km,imp),xor(kek,xor(pin,data)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,conjecture,
public(enc(pp,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ public(enc(pp,a)),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f32,plain,
! [U,V] :
( public(enc(enc(inv(xor(data,km)),U),V))
| ~ public(V)
| ~ public(U) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f33,plain,
! [X0,X1] :
( public(enc(enc(inv(xor(data,km)),X0),X1))
| ~ public(X1)
| ~ public(X0) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
! [U,V,W] :
( public(enc(xor(km,V),W))
| ~ public(enc(xor(km,imp),U))
| ~ public(enc(xor(U,V),W))
| ~ public(V) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f35,plain,
! [V,W] :
( public(enc(xor(km,V),W))
| ! [U] :
( ~ public(enc(xor(km,imp),U))
| ~ public(enc(xor(U,V),W))
| ~ public(V) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( public(enc(xor(km,X0),X2))
| ~ public(enc(xor(km,imp),X1))
| ~ public(enc(xor(X1,X0),X2))
| ~ public(X0) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f39,plain,
! [U,V] : enc(U,enc(inv(U),V)) = V,
inference(miniscoping,[status(thm)],[f8]) ).
fof(f40,plain,
! [X0,X1] : enc(X0,enc(inv(X0),X1)) = X1,
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
! [U,V] : xor(U,V) = xor(V,U),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f42,plain,
! [X0,X1] : xor(X0,X1) = xor(X1,X0),
inference(cnf_transformation,[status(thm)],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] : xor(X0,xor(X1,X2)) = xor(xor(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f44,plain,
! [U] : xor(U,U) = z,
inference(miniscoping,[status(thm)],[f11]) ).
fof(f45,plain,
! [X0] : xor(X0,X0) = z,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
! [U] : xor(U,z) = U,
inference(miniscoping,[status(thm)],[f12]) ).
fof(f47,plain,
! [X0] : xor(X0,z) = X0,
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
public(data),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f52,plain,
public(enc(xor(kek,pin),pp)),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f55,plain,
public(a),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f56,plain,
public(enc(xor(km,imp),xor(kek,xor(pin,data)))),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f57,plain,
~ public(enc(pp,a)),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f82,plain,
! [X0,X1] : enc(X0,X1) = enc(inv(inv(X0)),X1),
inference(paramodulation,[status(thm)],[f40,f40]) ).
fof(f378,plain,
! [X0,X1,X2] :
( public(enc(xor(X0,km),X2))
| ~ public(enc(xor(km,imp),X1))
| ~ public(enc(xor(X1,X0),X2))
| ~ public(X0) ),
inference(paramodulation,[status(thm)],[f42,f36]) ).
fof(f791,plain,
! [X0,X1] : enc(inv(X0),enc(X0,X1)) = X1,
inference(paramodulation,[status(thm)],[f82,f40]) ).
fof(f801,plain,
! [X0,X1] :
( public(enc(X0,X1))
| ~ public(X1)
| ~ public(enc(xor(data,km),X0)) ),
inference(paramodulation,[status(thm)],[f791,f33]) ).
fof(f1371,plain,
! [X0,X1,X2] :
( public(enc(X1,X2))
| ~ public(X2)
| ~ public(enc(xor(km,imp),X0))
| ~ public(enc(xor(X0,data),X1))
| ~ public(data) ),
inference(resolution,[status(thm)],[f378,f801]) ).
fof(f1388,plain,
! [X0,X1,X2] :
( public(enc(X1,X2))
| ~ public(X2)
| ~ public(enc(xor(km,imp),X0))
| ~ public(enc(xor(X0,data),X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1371,f49]) ).
fof(f1391,plain,
! [X0,X1] :
( public(enc(X0,X1))
| ~ public(X1)
| ~ public(enc(xor(xor(kek,xor(pin,data)),data),X0)) ),
inference(resolution,[status(thm)],[f1388,f56]) ).
fof(f1398,plain,
! [X0,X1] :
( public(enc(X0,X1))
| ~ public(X1)
| ~ public(enc(xor(kek,xor(xor(pin,data),data)),X0)) ),
inference(forward_demodulation,[status(thm)],[f43,f1391]) ).
fof(f1399,plain,
! [X0,X1] :
( public(enc(X0,X1))
| ~ public(X1)
| ~ public(enc(xor(kek,xor(pin,xor(data,data))),X0)) ),
inference(forward_demodulation,[status(thm)],[f43,f1398]) ).
fof(f1400,plain,
! [X0,X1] :
( public(enc(X0,X1))
| ~ public(X1)
| ~ public(enc(xor(kek,xor(pin,z)),X0)) ),
inference(forward_demodulation,[status(thm)],[f45,f1399]) ).
fof(f1401,plain,
! [X0,X1] :
( public(enc(X0,X1))
| ~ public(X1)
| ~ public(enc(xor(kek,pin),X0)) ),
inference(forward_demodulation,[status(thm)],[f47,f1400]) ).
fof(f1406,plain,
! [X0] :
( public(enc(pp,X0))
| ~ public(X0) ),
inference(resolution,[status(thm)],[f1401,f52]) ).
fof(f1411,plain,
~ public(a),
inference(resolution,[status(thm)],[f1406,f57]) ).
fof(f1414,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f1411,f55]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV234+2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 08:36:17 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.15/0.38 % Drodi V4.1.1
% 7.17/1.51 % Refutation found
% 7.17/1.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.17/1.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.17/1.54 % Elapsed time: 1.152541 seconds
% 7.17/1.54 % CPU time: 8.805652 seconds
% 7.17/1.54 % Total memory used: 115.624 MB
% 7.17/1.54 % Net memory used: 105.750 MB
%------------------------------------------------------------------------------