%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV236+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 0.09s 0.49s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 31 ( 18 unt; 0 def)
% Number of atoms : 50 ( 11 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 17 ~; 13 |; 4 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 1 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 : 41 ( 39 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X1,X2] : xor(X1,X2) = xor(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X1,X2,X3] : xor(X1,xor(X2,X3)) = xor(xor(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X1] : xor(X1,id) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X1] : xor(X1,X1) = id,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Xk,Xtype] :
( ( p(Xtype)
& p(Xk) )
=> p(crypt(xor(km,xor(kp,Xtype)),Xk)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [X1,X2] :
( ( p(X2)
& p(X1) )
=> p(xor(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
p(kp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
p(exp),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,conjecture,
? [X] :
( p(X)
& p(crypt(xor(km,exp),X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ? [X] :
( p(X)
& p(crypt(xor(km,exp),X)) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f30,plain,
! [X0,X1] : xor(X0,X1) = xor(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f31,plain,
! [X0,X1,X2] : xor(X0,xor(X1,X2)) = xor(xor(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f33,plain,
! [X0] : xor(X0,id) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f34,plain,
! [X0] : xor(X0,X0) = id,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f39,plain,
! [Xk,Xtype] :
( p(crypt(xor(km,xor(kp,Xtype)),Xk))
| ~ p(Xtype)
| ~ p(Xk) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f40,plain,
! [X0,X1] :
( p(crypt(xor(km,xor(kp,X1)),X0))
| ~ p(X1)
| ~ p(X0) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f52,plain,
! [X1,X2] :
( p(xor(X1,X2))
| ~ p(X2)
| ~ p(X1) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f53,plain,
! [X0,X1] :
( p(xor(X0,X1))
| ~ p(X1)
| ~ p(X0) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
fof(f61,plain,
p(kp),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f69,plain,
p(exp),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f71,plain,
! [X] :
( ~ p(X)
| ~ p(crypt(xor(km,exp),X)) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f72,plain,
! [X0] :
( ~ p(X0)
| ~ p(crypt(xor(km,exp),X0)) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f77,plain,
! [X0,X1,X2] : xor(X0,xor(X1,X2)) = xor(X2,xor(X0,X1)),
inference(paramodulation,[status(thm)],[f30,f31]) ).
fof(f134,plain,
! [X0] :
( p(xor(X0,exp))
| ~ p(X0) ),
inference(resolution,[status(thm)],[f53,f69]) ).
fof(f154,plain,
! [X0,X1] : xor(X0,xor(X0,X1)) = xor(X1,id),
inference(paramodulation,[status(thm)],[f34,f77]) ).
fof(f159,plain,
! [X0,X1] : xor(X0,xor(X0,X1)) = X1,
inference(forward_demodulation,[status(thm)],[f33,f154]) ).
fof(f997,plain,
p(xor(kp,exp)),
inference(resolution,[status(thm)],[f61,f134]) ).
fof(f1097,plain,
! [X0] :
( p(crypt(xor(km,xor(kp,xor(kp,exp))),X0))
| ~ p(X0) ),
inference(resolution,[status(thm)],[f997,f40]) ).
fof(f1113,plain,
! [X0] :
( p(crypt(xor(km,exp),X0))
| ~ p(X0) ),
inference(forward_demodulation,[status(thm)],[f159,f1097]) ).
fof(f1115,plain,
! [X0] : ~ p(X0),
inference(forward_subsumption_resolution,[status(thm)],[f1113,f72]) ).
fof(f1116,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f997,f1115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV236+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n019.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 08:35:50 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.49 % Refutation found
% 0.09/0.49 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.50 % Elapsed time: 0.119543 seconds
% 0.09/0.50 % CPU time: 0.697172 seconds
% 0.09/0.50 % Total memory used: 74.958 MB
% 0.09/0.50 % Net memory used: 73.276 MB
%------------------------------------------------------------------------------