%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWV235+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 2.83s 0.83s
% Output : CNFRefutation 2.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 52 ( 23 unt; 0 def)
% Number of atoms : 122 ( 7 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 133 ( 63 ~; 58 |; 7 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-2 aty)
% Number of variables : 73 ( 73 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X1,X2] : xor(X1,X2) = xor(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X1] : xor(X1,id) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X1] : xor(X1,X1) = id,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [Xtype,Xk1,Xkek1] :
( ( p(crypt(xor(km,exp),Xkek1))
& p(Xtype)
& p(crypt(xor(km,Xtype),Xk1)) )
=> p(crypt(xor(Xkek1,Xtype),Xk1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Xk,Xtype] :
( ( p(Xtype)
& p(Xk) )
=> p(crypt(xor(km,xor(kp,Xtype)),Xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Xk1,Xtype,Xk2] :
( ( p(Xtype)
& p(crypt(xor(km,xor(Xtype,kp)),Xk2))
& p(Xk1) )
=> p(crypt(xor(km,Xtype),xor(Xk2,Xk1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X1,X2] :
( ( p(X1)
& p(crypt(X1,X2)) )
=> p(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [X1,X2] :
( ( p(X1)
& p(X2) )
=> p(crypt(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
p(pin),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
p(crypt(xor(km,pin),pp)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
p(crypt(xor(km,imp),rand)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
p(exp),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
p(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
p(crypt(pp,a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ p(crypt(pp,a)),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f31,plain,
! [X0,X1] : xor(X0,X1) = xor(X1,X0),
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f34,plain,
! [X0] : xor(X0,id) = X0,
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f35,plain,
! [X0] : xor(X0,X0) = id,
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f38,plain,
! [Xtype,Xk1,Xkek1] :
( p(crypt(xor(Xkek1,Xtype),Xk1))
| ~ p(crypt(xor(km,exp),Xkek1))
| ~ p(Xtype)
| ~ p(crypt(xor(km,Xtype),Xk1)) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f39,plain,
! [X0,X1,X2] :
( p(crypt(xor(X2,X0),X1))
| ~ p(crypt(xor(km,exp),X2))
| ~ p(X0)
| ~ p(crypt(xor(km,X0),X1)) ),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
! [Xk,Xtype] :
( p(crypt(xor(km,xor(kp,Xtype)),Xk))
| ~ p(Xtype)
| ~ p(Xk) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f41,plain,
! [X0,X1] :
( p(crypt(xor(km,xor(kp,X1)),X0))
| ~ p(X1)
| ~ p(X0) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f44,plain,
! [Xk1,Xtype,Xk2] :
( p(crypt(xor(km,Xtype),xor(Xk2,Xk1)))
| ~ p(Xtype)
| ~ p(crypt(xor(km,xor(Xtype,kp)),Xk2))
| ~ p(Xk1) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f45,plain,
! [X0,X1,X2] :
( p(crypt(xor(km,X1),xor(X2,X0)))
| ~ p(X1)
| ~ p(crypt(xor(km,xor(X1,kp)),X2))
| ~ p(X0) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f55,plain,
! [X1,X2] :
( p(X2)
| ~ p(X1)
| ~ p(crypt(X1,X2)) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f56,plain,
! [X2] :
( p(X2)
| ! [X1] :
( ~ p(X1)
| ~ p(crypt(X1,X2)) ) ),
inference(miniscoping,[status(thm)],[f55]) ).
fof(f57,plain,
! [X0,X1] :
( p(X1)
| ~ p(X0)
| ~ p(crypt(X0,X1)) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f58,plain,
! [X1,X2] :
( p(crypt(X1,X2))
| ~ p(X1)
| ~ p(X2) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f59,plain,
! [X0,X1] :
( p(crypt(X1,X0))
| ~ p(X1)
| ~ p(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f64,plain,
p(pin),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f65,plain,
p(crypt(xor(km,pin),pp)),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f67,plain,
p(crypt(xor(km,imp),rand)),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f70,plain,
p(exp),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f71,plain,
p(a),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f72,plain,
~ p(crypt(pp,a)),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f77,plain,
! [X0] : xor(id,X0) = X0,
inference(paramodulation,[status(thm)],[f31,f34]) ).
fof(f180,plain,
( ~ p(pp)
| ~ p(a) ),
inference(resolution,[status(thm)],[f59,f72]) ).
fof(f182,plain,
~ p(pp),
inference(forward_subsumption_resolution,[status(thm)],[f180,f71]) ).
fof(f424,plain,
! [X0,X1] :
( p(crypt(xor(km,xor(X1,kp)),X0))
| ~ p(X1)
| ~ p(X0) ),
inference(paramodulation,[status(thm)],[f31,f41]) ).
fof(f858,plain,
! [X0,X1,X2] :
( p(crypt(xor(km,X1),xor(X0,X2)))
| ~ p(X1)
| ~ p(X2)
| ~ p(X1)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f424,f45]) ).
fof(f871,plain,
! [X0,X1,X2] :
( p(crypt(xor(km,X1),xor(X0,X2)))
| ~ p(X2)
| ~ p(X1)
| ~ p(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f858]) ).
fof(f1003,plain,
! [X0,X1] :
( p(crypt(xor(km,X1),id))
| ~ p(X0)
| ~ p(X1)
| ~ p(X0) ),
inference(paramodulation,[status(thm)],[f35,f871]) ).
fof(f1012,plain,
! [X0,X1] :
( p(crypt(xor(km,X1),id))
| ~ p(X1)
| ~ p(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1003]) ).
fof(f1016,plain,
! [X0,X1,X2] :
( p(crypt(xor(id,X1),X2))
| ~ p(X1)
| ~ p(crypt(xor(km,X1),X2))
| ~ p(exp)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f1012,f39]) ).
fof(f1035,plain,
! [X0,X1,X2] :
( p(crypt(X1,X2))
| ~ p(X1)
| ~ p(crypt(xor(km,X1),X2))
| ~ p(exp)
| ~ p(X0) ),
inference(forward_demodulation,[status(thm)],[f77,f1016]) ).
fof(f1036,plain,
! [X0,X1,X2] :
( p(crypt(X1,X2))
| ~ p(X1)
| ~ p(crypt(xor(km,X1),X2))
| ~ p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1035,f70]) ).
fof(f1105,plain,
! [X0] :
( p(crypt(pin,pp))
| ~ p(pin)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f1036,f65]) ).
fof(f1132,plain,
! [X0] :
( p(crypt(pin,pp))
| ~ p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1105,f64]) ).
fof(f1142,plain,
! [X0] :
( p(pp)
| ~ p(pin)
| ~ p(X0) ),
inference(resolution,[status(thm)],[f1132,f57]) ).
fof(f1143,plain,
! [X0] :
( p(pp)
| ~ p(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1142,f64]) ).
fof(f1145,plain,
! [X0] : ~ p(X0),
inference(forward_subsumption_resolution,[status(thm)],[f1143,f182]) ).
fof(f1146,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f67,f1145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV235+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n011.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 08:35:10 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 2.83/0.83 % Refutation found
% 2.83/0.83 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.83/0.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.58/0.85 % Elapsed time: 0.486327 seconds
% 2.58/0.85 % CPU time: 3.570167 seconds
% 2.58/0.85 % Total memory used: 100.758 MB
% 2.58/0.85 % Net memory used: 91.655 MB
%------------------------------------------------------------------------------