%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV233+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n007.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 : Fri Sep 25 03:16:44 PM UTC 2026
% Result : Theorem 0.85s 1.29s
% Output : CNFRefutation 0.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 15
% Syntax : Number of formulae : 144 ( 42 unt; 0 def)
% Number of atoms : 434 ( 54 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 537 ( 247 ~; 240 |; 42 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 9 con; 0-2 aty)
% Number of variables : 237 ( 0 sgn 237 !; 0 ?; 141 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ( knows(inverse(X1))
& knows(encrypt(X0,X1)) )
=> knows(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',encrypt_equation) ).
fof(f2,axiom,
! [X0,X1] :
( ( knows(X1)
& knows(symmetric_encrypt(X0,X1)) )
=> knows(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_encrypt_equation) ).
fof(f3,axiom,
! [X0,X1] :
( ( knows(X1)
& knows(sign(X0,inverse(X1))) )
=> knows(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sign_equation) ).
fof(f4,axiom,
! [X0,X1] :
( ( knows(X1)
& knows(X0) )
=> ( knows(sign(X0,X1))
& knows(extract(X0,X1))
& knows(symmetric_decrypt(X0,X1))
& knows(decrypt(X0,X1))
& knows(symmetric_encrypt(X0,X1))
& knows(encrypt(X0,X1))
& knows(concatenate(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',construct_message_1) ).
fof(f5,axiom,
! [X0,X1] :
( knows(concatenate(X0,X1))
=> ( knows(X1)
& knows(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',construct_message_2) ).
fof(f6,axiom,
! [X0] :
( knows(X0)
=> ( knows(hash(X0))
& knows(tail(X0))
& knows(head(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',construct_message_3) ).
fof(f7,axiom,
! [X0,X1] : decrypt(encrypt(X0,X1),inverse(X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',decrypt_axiom) ).
fof(f9,axiom,
! [X0,X1] : extract(sign(X0,inverse(X1)),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sign_axiom) ).
fof(f10,axiom,
! [X0,X1] : head(concatenate(X0,X1)) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',head_axiom) ).
fof(f11,axiom,
! [X0,X1] : tail(concatenate(X0,X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tail_axiom) ).
fof(f12,axiom,
! [X0] : first(X0) = head(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',first_axiom) ).
fof(f13,axiom,
! [X0] : second(X0) = head(tail(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',second_axiom) ).
fof(f17,axiom,
( knows(k_a)
& knows(inverse(k_a))
& knows(k_ca) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',previous_knowledge) ).
fof(f18,axiom,
! [X0,X1,X2,X3,X4] :
( ( ( second(extract(X2,X1)) = X1
& knows(X2)
& knows(X1)
& knows(X0) )
=> knows(concatenate(encrypt(sign(concatenate(kgen(X1),concatenate(X0,eol)),inverse(k_s)),X1),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca)))) )
& ( ( second(extract(decrypt(X3,inverse(k_c)),second(extract(X4,k_ca)))) = n
& first(extract(X4,k_ca)) = s
& knows(X4)
& knows(X3) )
=> knows(symmetric_encrypt(secret,first(extract(decrypt(X3,inverse(k_c)),second(extract(X4,k_ca)))))) )
& knows(concatenate(n,concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c))))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',protocol) ).
fof(f19,conjecture,
knows(secret),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',attack) ).
fof(f20,negated_conjecture,
~ knows(secret),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
~ knows(secret),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ~ knows(inverse(X1))
| ~ knows(encrypt(X0,X1))
| knows(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f23,plain,
! [X0,X1] :
( ~ knows(inverse(X1))
| ~ knows(encrypt(X0,X1))
| knows(X0) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ~ knows(X1)
| ~ knows(symmetric_encrypt(X0,X1))
| knows(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f25,plain,
! [X0,X1] :
( ~ knows(X1)
| ~ knows(symmetric_encrypt(X0,X1))
| knows(X0) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
! [X0,X1] :
( ~ knows(X1)
| ~ knows(sign(X0,inverse(X1)))
| knows(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f27,plain,
! [X0,X1] :
( ~ knows(X1)
| ~ knows(sign(X0,inverse(X1)))
| knows(X0) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( ~ knows(X1)
| ~ knows(X0)
| ( knows(sign(X0,X1))
& knows(extract(X0,X1))
& knows(symmetric_decrypt(X0,X1))
& knows(decrypt(X0,X1))
& knows(symmetric_encrypt(X0,X1))
& knows(encrypt(X0,X1))
& knows(concatenate(X0,X1)) ) ),
inference(ennf_transformation,[],[f4]) ).
fof(f29,plain,
! [X0,X1] :
( ~ knows(X1)
| ~ knows(X0)
| ( knows(sign(X0,X1))
& knows(extract(X0,X1))
& knows(symmetric_decrypt(X0,X1))
& knows(decrypt(X0,X1))
& knows(symmetric_encrypt(X0,X1))
& knows(encrypt(X0,X1))
& knows(concatenate(X0,X1)) ) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
! [X0,X1] :
( ~ knows(concatenate(X0,X1))
| ( knows(X1)
& knows(X0) ) ),
inference(ennf_transformation,[],[f5]) ).
fof(f31,plain,
! [X0] :
( ~ knows(X0)
| ( knows(hash(X0))
& knows(tail(X0))
& knows(head(X0)) ) ),
inference(ennf_transformation,[],[f6]) ).
fof(f34,plain,
! [X0,X1,X2,X3,X4] :
( ( second(extract(X2,X1)) != X1
| ~ knows(X2)
| ~ knows(X1)
| ~ knows(X0)
| knows(concatenate(encrypt(sign(concatenate(kgen(X1),concatenate(X0,eol)),inverse(k_s)),X1),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca)))) )
& ( n != second(extract(decrypt(X3,inverse(k_c)),second(extract(X4,k_ca))))
| first(extract(X4,k_ca)) != s
| ~ knows(X4)
| ~ knows(X3)
| knows(symmetric_encrypt(secret,first(extract(decrypt(X3,inverse(k_c)),second(extract(X4,k_ca)))))) )
& knows(concatenate(n,concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c))))) ),
inference(ennf_transformation,[],[f18]) ).
fof(f35,plain,
! [X0,X1,X2,X3,X4] :
( ( second(extract(X2,X1)) != X1
| ~ knows(X2)
| ~ knows(X1)
| ~ knows(X0)
| knows(concatenate(encrypt(sign(concatenate(kgen(X1),concatenate(X0,eol)),inverse(k_s)),X1),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca)))) )
& ( n != second(extract(decrypt(X3,inverse(k_c)),second(extract(X4,k_ca))))
| first(extract(X4,k_ca)) != s
| ~ knows(X4)
| ~ knows(X3)
| knows(symmetric_encrypt(secret,first(extract(decrypt(X3,inverse(k_c)),second(extract(X4,k_ca)))))) )
& knows(concatenate(n,concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c))))) ),
inference(flattening,[],[f34]) ).
fof(f36,plain,
! [X0,X1] :
( ~ knows(inverse(X1))
| ~ knows(encrypt(X0,X1))
| knows(X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f37,plain,
! [X0,X1] :
( ~ knows(X1)
| ~ knows(symmetric_encrypt(X0,X1))
| knows(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f38,plain,
! [X0,X1] :
( ~ knows(X1)
| ~ knows(sign(X0,inverse(X1)))
| knows(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f39,plain,
! [X0,X1] :
( ~ knows(X1)
| ~ knows(X0)
| knows(sign(X0,X1)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f44,plain,
! [X0,X1] :
( ~ knows(X1)
| ~ knows(X0)
| knows(encrypt(X0,X1)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f45,plain,
! [X0,X1] :
( ~ knows(X1)
| ~ knows(X0)
| knows(concatenate(X0,X1)) ),
inference(cnf_transformation,[],[f29]) ).
fof(f46,plain,
! [X0,X1] :
( ~ knows(concatenate(X0,X1))
| knows(X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f47,plain,
! [X0,X1] :
( ~ knows(concatenate(X0,X1))
| knows(X0) ),
inference(cnf_transformation,[],[f30]) ).
fof(f50,plain,
! [X0] :
( ~ knows(X0)
| knows(head(X0)) ),
inference(cnf_transformation,[],[f31]) ).
fof(f51,plain,
! [X0,X1] : decrypt(encrypt(X0,X1),inverse(X1)) = X0,
inference(cnf_transformation,[],[f7]) ).
fof(f53,plain,
! [X0,X1] : extract(sign(X0,inverse(X1)),X1) = X0,
inference(cnf_transformation,[],[f9]) ).
fof(f54,plain,
! [X0,X1] : head(concatenate(X0,X1)) = X0,
inference(cnf_transformation,[],[f10]) ).
fof(f55,plain,
! [X0,X1] : tail(concatenate(X0,X1)) = X1,
inference(cnf_transformation,[],[f11]) ).
fof(f56,plain,
! [X0] : head(X0) = first(X0),
inference(cnf_transformation,[],[f12]) ).
fof(f57,plain,
! [X0] : second(X0) = head(tail(X0)),
inference(cnf_transformation,[],[f13]) ).
fof(f61,plain,
knows(k_a),
inference(cnf_transformation,[],[f17]) ).
fof(f62,plain,
knows(inverse(k_a)),
inference(cnf_transformation,[],[f17]) ).
fof(f63,plain,
knows(k_ca),
inference(cnf_transformation,[],[f17]) ).
fof(f64,plain,
! [X2,X0,X1] :
( second(extract(X2,X1)) != X1
| ~ knows(X2)
| ~ knows(X1)
| ~ knows(X0)
| knows(concatenate(encrypt(sign(concatenate(kgen(X1),concatenate(X0,eol)),inverse(k_s)),X1),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca)))) ),
inference(cnf_transformation,[],[f35]) ).
fof(f65,plain,
! [X3,X4] :
( n != second(extract(decrypt(X3,inverse(k_c)),second(extract(X4,k_ca))))
| first(extract(X4,k_ca)) != s
| ~ knows(X4)
| ~ knows(X3)
| knows(symmetric_encrypt(secret,first(extract(decrypt(X3,inverse(k_c)),second(extract(X4,k_ca)))))) ),
inference(cnf_transformation,[],[f35]) ).
fof(f66,plain,
knows(concatenate(n,concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c))))),
inference(cnf_transformation,[],[f35]) ).
fof(f67,plain,
~ knows(secret),
inference(cnf_transformation,[],[f21]) ).
fof(f69,plain,
! [X0] : second(X0) = first(tail(X0)),
inference(definition_unfolding,[],[f57,f56]) ).
fof(f71,plain,
! [X0] :
( ~ knows(X0)
| knows(first(X0)) ),
inference(definition_unfolding,[],[f50,f56]) ).
fof(f72,plain,
! [X0,X1] : first(concatenate(X0,X1)) = X0,
inference(definition_unfolding,[],[f54,f56]) ).
fof(f73,plain,
! [X3,X4] :
( n != first(tail(extract(decrypt(X3,inverse(k_c)),first(tail(extract(X4,k_ca))))))
| first(extract(X4,k_ca)) != s
| ~ knows(X4)
| ~ knows(X3)
| knows(symmetric_encrypt(secret,first(extract(decrypt(X3,inverse(k_c)),first(tail(extract(X4,k_ca))))))) ),
inference(definition_unfolding,[],[f65,f69,f69,f69]) ).
fof(f74,plain,
! [X2,X0,X1] :
( first(tail(extract(X2,X1))) != X1
| ~ knows(X2)
| ~ knows(X1)
| ~ knows(X0)
| knows(concatenate(encrypt(sign(concatenate(kgen(X1),concatenate(X0,eol)),inverse(k_s)),X1),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca)))) ),
inference(definition_unfolding,[],[f64,f69]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( knows(X0)
| ~ knows(inverse(X1))
| ~ knows(encrypt(X0,X1)) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( knows(X0)
| ~ knows(X1)
| ~ knows(symmetric_encrypt(X0,X1)) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] :
( knows(X0)
| ~ knows(X1)
| ~ knows(sign(X0,inverse(X1))) ),
inference(cnf_transformation,[],[f38]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( knows(concatenate(X0,X1))
| ~ knows(X1)
| ~ knows(X0) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i] :
( knows(encrypt(X0,X1))
| ~ knows(X1)
| ~ knows(X0) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( knows(sign(X0,X1))
| ~ knows(X1)
| ~ knows(X0) ),
inference(cnf_transformation,[],[f39]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i] :
( knows(X0)
| ~ knows(concatenate(X0,X1)) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( knows(X1)
| ~ knows(concatenate(X0,X1)) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_61,plain,
! [X0: $i] :
( knows(first(X0))
| ~ knows(X0) ),
inference(cnf_transformation,[],[f71]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : decrypt(encrypt(X0,X1),inverse(X1)) = X0,
inference(cnf_transformation,[],[f51]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] : extract(sign(X0,inverse(X1)),X1) = X0,
inference(cnf_transformation,[],[f53]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] : first(concatenate(X0,X1)) = X0,
inference(cnf_transformation,[],[f72]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] : tail(concatenate(X0,X1)) = X1,
inference(cnf_transformation,[],[f55]) ).
tcf(c_70,plain,
knows(k_ca),
inference(cnf_transformation,[],[f63]) ).
tcf(c_71,plain,
knows(inverse(k_a)),
inference(cnf_transformation,[],[f62]) ).
tcf(c_72,plain,
knows(k_a),
inference(cnf_transformation,[],[f61]) ).
tcf(c_73,plain,
knows(concatenate(n,concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c))))),
inference(cnf_transformation,[],[f66]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i] :
( knows(symmetric_encrypt(secret,first(extract(decrypt(X1,inverse(k_c)),first(tail(extract(X0,k_ca)))))))
| ~ knows(X1)
| ~ knows(X0)
| ( first(extract(X0,k_ca)) != s )
| ( first(tail(extract(decrypt(X1,inverse(k_c)),first(tail(extract(X0,k_ca)))))) != n ) ),
inference(cnf_transformation,[],[f73]) ).
tcf(c_75,plain,
! [X0: $i,X1: $i,X2: $i] :
( knows(concatenate(encrypt(sign(concatenate(kgen(X1),concatenate(X2,eol)),inverse(k_s)),X1),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| ~ knows(X2)
| ~ knows(X1)
| ~ knows(X0)
| ( first(tail(extract(X0,X1))) != X1 ) ),
inference(cnf_transformation,[],[f74]) ).
tcf(c_76,negated_conjecture,
~ knows(secret),
inference(cnf_transformation,[],[f67]) ).
tcf(c_109,plain,
! [X0: $i,X1: $i] :
( knows(first(X0))
| ~ knows(concatenate(X0,X1)) ),
inference(prop_impl_just,[status(thm)],[c_61,c_59]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_10(X1)
| ( first(tail(extract(X0,X1))) != X1 )
| ~ knows(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_75]) ).
tcf(c_159,plain,
! [X0: $i,X1: $i] :
( iPr_def_10(X0)
| knows(concatenate(encrypt(sign(concatenate(kgen(X0),concatenate(X1,eol)),inverse(k_s)),X0),sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))))
| ~ knows(X1)
| ~ knows(X0) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_75]) ).
tcf(c_379,plain,
knows(first(n)),
inference(superposition,[status(thm)],[c_73,c_109]) ).
tcf(c_382,plain,
knows(n),
inference(superposition,[status(thm)],[c_73,c_59]) ).
tcf(c_383,plain,
knows(concatenate(k_c,sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c)))),
inference(superposition,[status(thm)],[c_73,c_60]) ).
tcf(c_387,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_10(X1)
| ~ knows(sign(X0,inverse(X1)))
| ( first(tail(X0)) != X1 ) ),
inference(superposition,[status(thm)],[c_66,c_158]) ).
tcf(c_401,plain,
! [X0: $i,X1: $i] :
( iPr_def_10(X0)
| knows(encrypt(sign(concatenate(kgen(X0),concatenate(X1,eol)),inverse(k_s)),X0))
| ~ knows(X1)
| ~ knows(X0) ),
inference(superposition,[status(thm)],[c_159,c_59]) ).
tcf(c_402,plain,
! [X0: $i,X1: $i] :
( iPr_def_10(X0)
| knows(sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca)))
| ~ knows(X1)
| ~ knows(X0) ),
inference(superposition,[status(thm)],[c_159,c_60]) ).
tcf(c_443,plain,
( iPr_def_10(k_c)
| knows(sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca)))
| ~ knows(k_c) ),
inference(instantiation,[status(thm)],[c_402]) ).
tcf(c_472,plain,
! [X0: $i,X1: $i] :
( knows(symmetric_encrypt(secret,first(extract(decrypt(X0,inverse(k_c)),first(tail(extract(sign(X1,inverse(k_ca)),k_ca)))))))
| ~ knows(X0)
| ~ knows(sign(X1,inverse(k_ca)))
| ( first(extract(sign(X1,inverse(k_ca)),k_ca)) != s )
| ( first(tail(extract(decrypt(X0,inverse(k_c)),first(tail(X1))))) != n ) ),
inference(superposition,[status(thm)],[c_66,c_74]) ).
tcf(c_499,plain,
! [X0: $i,X1: $i] :
( knows(symmetric_encrypt(secret,first(extract(decrypt(X0,inverse(k_c)),first(tail(X1))))))
| ~ knows(X0)
| ~ knows(sign(X1,inverse(k_ca)))
| ( first(X1) != s )
| ( first(tail(extract(decrypt(X0,inverse(k_c)),first(tail(X1))))) != n ) ),
inference(demodulation,[status(thm)],[c_472,c_66]) ).
tcf(c_518,plain,
knows(k_c),
inference(superposition,[status(thm)],[c_383,c_59]) ).
tcf(c_519,plain,
knows(sign(concatenate(c,concatenate(k_c,eol)),inverse(k_c))),
inference(superposition,[status(thm)],[c_383,c_60]) ).
tcf(c_523,plain,
! [X0: $i] :
( ~ iPr_def_10(first(tail(X0)))
| ~ knows(sign(X0,inverse(first(tail(X0))))) ),
inference(unflattening,[status(thm)],[c_387]) ).
tcf(c_527,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_10(first(tail(concatenate(X0,X1))))
| ~ knows(sign(concatenate(X0,X1),inverse(first(X1)))) ),
inference(superposition,[status(thm)],[c_68,c_523]) ).
tcf(c_538,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_10(first(X1))
| ~ knows(sign(concatenate(X0,X1),inverse(first(X1)))) ),
inference(demodulation,[status(thm)],[c_527,c_68]) ).
tcf(c_566,plain,
! [X0: $i] :
( iPr_def_10(X0)
| knows(sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca)))
| ~ knows(X0) ),
inference(superposition,[status(thm)],[c_379,c_402]) ).
tcf(c_595,plain,
! [X0: $i,X1: $i] :
( iPr_def_10(X0)
| knows(sign(concatenate(kgen(X0),concatenate(X1,eol)),inverse(k_s)))
| ~ knows(X1)
| ~ knows(X0)
| ~ knows(inverse(X0)) ),
inference(superposition,[status(thm)],[c_401,c_49]) ).
tcf(c_748,plain,
! [X0: $i,X1: $i,X2: $i] :
( knows(symmetric_encrypt(secret,first(extract(decrypt(X0,inverse(k_c)),first(tail(concatenate(X2,X1)))))))
| ~ knows(X0)
| ~ knows(sign(concatenate(X2,X1),inverse(k_ca)))
| ( first(concatenate(X2,X1)) != s )
| ( first(tail(extract(decrypt(X0,inverse(k_c)),first(X1)))) != n ) ),
inference(superposition,[status(thm)],[c_68,c_499]) ).
tcf(c_770,plain,
! [X0: $i,X1: $i,X2: $i] :
( knows(symmetric_encrypt(secret,first(extract(decrypt(X0,inverse(k_c)),first(X1)))))
| ~ knows(X0)
| ~ knows(sign(concatenate(X2,X1),inverse(k_ca)))
| ( X2 != s )
| ( first(tail(extract(decrypt(X0,inverse(k_c)),first(X1)))) != n ) ),
inference(demodulation,[status(thm)],[c_748,c_67,c_68]) ).
tcf(c_805,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ iPr_def_10(first(concatenate(X1,X2)))
| ~ knows(sign(concatenate(X0,concatenate(X1,X2)),inverse(X1))) ),
inference(superposition,[status(thm)],[c_67,c_538]) ).
tcf(c_816,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ iPr_def_10(X1)
| ~ knows(sign(concatenate(X0,concatenate(X1,X2)),inverse(X1))) ),
inference(demodulation,[status(thm)],[c_805,c_67]) ).
tcf(c_862,plain,
( iPr_def_10(n)
| knows(sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))) ),
inference(superposition,[status(thm)],[c_382,c_566]) ).
tcf(c_1107,plain,
! [X0: $i,X1: $i] :
( iPr_def_10(X0)
| knows(encrypt(sign(concatenate(kgen(X0),concatenate(X1,eol)),inverse(k_s)),X0))
| ~ knows(X1)
| ~ knows(X0) ),
inference(superposition,[status(thm)],[c_159,c_59]) ).
tcf(c_1170,plain,
! [X0: $i,X1: $i] :
( iPr_def_10(X0)
| knows(concatenate(kgen(X0),concatenate(X1,eol)))
| ~ knows(k_s)
| ~ knows(X1)
| ~ knows(X0)
| ~ knows(inverse(X0)) ),
inference(superposition,[status(thm)],[c_595,c_51]) ).
tcf(c_1338,plain,
! [X0: $i,X1: $i] :
( knows(symmetric_encrypt(secret,first(extract(decrypt(X0,inverse(k_c)),first(X1)))))
| ~ knows(X0)
| ~ knows(sign(concatenate(s,X1),inverse(k_ca)))
| ( first(tail(extract(decrypt(X0,inverse(k_c)),first(X1)))) != n ) ),
inference(unflattening,[status(thm)],[c_770]) ).
tcf(c_1343,plain,
! [X0: $i,X1: $i] :
( knows(symmetric_encrypt(secret,first(extract(decrypt(encrypt(X0,k_c),inverse(k_c)),first(X1)))))
| ~ knows(encrypt(X0,k_c))
| ~ knows(sign(concatenate(s,X1),inverse(k_ca)))
| ( first(tail(extract(X0,first(X1)))) != n ) ),
inference(superposition,[status(thm)],[c_64,c_1338]) ).
tcf(c_1353,plain,
! [X0: $i,X1: $i] :
( knows(symmetric_encrypt(secret,first(extract(X0,first(X1)))))
| ~ knows(encrypt(X0,k_c))
| ~ knows(sign(concatenate(s,X1),inverse(k_ca)))
| ( first(tail(extract(X0,first(X1)))) != n ) ),
inference(demodulation,[status(thm)],[c_1343,c_64]) ).
tcf(c_1386,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ iPr_def_10(X1)
| ~ knows(inverse(X1))
| ~ knows(concatenate(X0,concatenate(X1,X2))) ),
inference(superposition,[status(thm)],[c_58,c_816]) ).
tcf(c_1387,plain,
~ iPr_def_10(k_c),
inference(superposition,[status(thm)],[c_519,c_816]) ).
tcf(c_1455,plain,
knows(sign(concatenate(s,concatenate(k_s,eol)),inverse(k_ca))),
inference(global_subsumption_just,[status(thm)],[c_862,c_443,c_518,c_1387]) ).
tcf(c_1459,plain,
( knows(concatenate(s,concatenate(k_s,eol)))
| ~ knows(k_ca) ),
inference(superposition,[status(thm)],[c_1455,c_51]) ).
tcf(c_1515,plain,
! [X0: $i,X1: $i] :
( iPr_def_10(X0)
| knows(kgen(X0))
| ~ knows(k_s)
| ~ knows(X1)
| ~ knows(X0)
| ~ knows(inverse(X0)) ),
inference(superposition,[status(thm)],[c_1170,c_59]) ).
tcf(c_1516,plain,
! [X0: $i,X1: $i] :
( iPr_def_10(X0)
| knows(concatenate(X1,eol))
| ~ knows(k_s)
| ~ knows(X1)
| ~ knows(X0)
| ~ knows(inverse(X0)) ),
inference(superposition,[status(thm)],[c_1170,c_60]) ).
tcf(c_1641,plain,
! [X0: $i,X1: $i] :
( knows(symmetric_encrypt(secret,first(extract(sign(X0,inverse(first(X1))),first(X1)))))
| ~ knows(sign(concatenate(s,X1),inverse(k_ca)))
| ~ knows(encrypt(sign(X0,inverse(first(X1))),k_c))
| ( first(tail(X0)) != n ) ),
inference(superposition,[status(thm)],[c_66,c_1353]) ).
tcf(c_1664,plain,
! [X0: $i,X1: $i] :
( knows(symmetric_encrypt(secret,first(X0)))
| ~ knows(sign(concatenate(s,X1),inverse(k_ca)))
| ~ knows(encrypt(sign(X0,inverse(first(X1))),k_c))
| ( first(tail(X0)) != n ) ),
inference(demodulation,[status(thm)],[c_1641,c_66]) ).
tcf(c_1717,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ iPr_def_10(X0)
| ~ knows(X2)
| ~ knows(inverse(X0))
| ~ knows(concatenate(X0,X1)) ),
inference(superposition,[status(thm)],[c_52,c_1386]) ).
tcf(c_1789,plain,
knows(concatenate(s,concatenate(k_s,eol))),
inference(global_subsumption_just,[status(thm)],[c_1459,c_70,c_1459]) ).
tcf(c_1798,plain,
knows(concatenate(k_s,eol)),
inference(superposition,[status(thm)],[c_1789,c_60]) ).
tcf(c_1846,plain,
! [X0: $i] :
( iPr_def_10(k_a)
| knows(concatenate(X0,eol))
| ~ knows(k_s)
| ~ knows(k_a)
| ~ knows(X0) ),
inference(superposition,[status(thm)],[c_71,c_1516]) ).
tcf(c_1973,plain,
! [X0: $i,X1: $i] :
( iPr_def_10(X0)
| knows(sign(concatenate(kgen(X0),concatenate(X1,eol)),inverse(k_s)))
| ~ knows(X1)
| ~ knows(X0)
| ~ knows(inverse(X0)) ),
inference(superposition,[status(thm)],[c_1107,c_49]) ).
tcf(c_2076,plain,
! [X0: $i,X1: $i,X2: $i] :
( knows(symmetric_encrypt(secret,first(concatenate(X1,X0))))
| ~ knows(sign(concatenate(s,X2),inverse(k_ca)))
| ~ knows(encrypt(sign(concatenate(X1,X0),inverse(first(X2))),k_c))
| ( first(X0) != n ) ),
inference(superposition,[status(thm)],[c_68,c_1664]) ).
tcf(c_2081,plain,
! [X0: $i,X1: $i,X2: $i] :
( knows(symmetric_encrypt(secret,X1))
| ~ knows(sign(concatenate(s,X2),inverse(k_ca)))
| ~ knows(encrypt(sign(concatenate(X1,X0),inverse(first(X2))),k_c))
| ( first(X0) != n ) ),
inference(demodulation,[status(thm)],[c_2076,c_67]) ).
tcf(c_2121,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ iPr_def_10(X0)
| ~ knows(X2)
| ~ knows(X1)
| ~ knows(X0)
| ~ knows(inverse(X0)) ),
inference(superposition,[status(thm)],[c_52,c_1717]) ).
tcf(c_2277,plain,
knows(k_s),
inference(superposition,[status(thm)],[c_1798,c_59]) ).
tcf(c_2298,plain,
! [X0: $i] :
( iPr_def_10(k_a)
| knows(concatenate(X0,eol))
| ~ knows(X0) ),
inference(global_subsumption_just,[status(thm)],[c_1846,c_72,c_1846,c_2277]) ).
tcf(c_2308,plain,
! [X0: $i,X1: $i] :
( iPr_def_10(k_a)
| ~ iPr_def_10(X0)
| ~ knows(X1)
| ~ knows(X0)
| ~ knows(inverse(X0)) ),
inference(superposition,[status(thm)],[c_2298,c_1717]) ).
tcf(c_2460,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( knows(symmetric_encrypt(secret,X1))
| ~ knows(sign(concatenate(s,X3),inverse(k_ca)))
| ~ knows(encrypt(sign(concatenate(X1,concatenate(X0,X2)),inverse(first(X3))),k_c))
| ( X0 != n ) ),
inference(superposition,[status(thm)],[c_67,c_2081]) ).
tcf(c_2513,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_10(k_a)
| ~ knows(k_a)
| ~ knows(X1)
| ~ knows(X0) ),
inference(superposition,[status(thm)],[c_71,c_2121]) ).
tcf(c_2518,plain,
( ~ iPr_def_10(k_a)
| ~ knows(k_c)
| ~ knows(k_a) ),
inference(instantiation,[status(thm)],[c_2513]) ).
tcf(c_2591,plain,
! [X0: $i,X1: $i] :
( ~ knows(inverse(X0))
| ~ knows(X0)
| ~ knows(X1)
| ~ iPr_def_10(X0) ),
inference(global_subsumption_just,[status(thm)],[c_2308,c_72,c_518,c_2308,c_2518]) ).
tcf(c_2592,plain,
! [X0: $i,X1: $i] :
( ~ iPr_def_10(X0)
| ~ knows(X1)
| ~ knows(X0)
| ~ knows(inverse(X0)) ),
inference(renaming,[status(thm)],[c_2591]) ).
tcf(c_2601,plain,
! [X0: $i,X1: $i,X2: $i] :
( knows(symmetric_encrypt(secret,X0))
| ~ knows(sign(concatenate(s,X2),inverse(k_ca)))
| ~ knows(encrypt(sign(concatenate(X0,concatenate(n,X1)),inverse(first(X2))),k_c)) ),
inference(unflattening,[status(thm)],[c_2460]) ).
tcf(c_2605,plain,
! [X0: $i,X1: $i,X2: $i] :
( knows(symmetric_encrypt(secret,X0))
| ~ knows(k_c)
| ~ knows(sign(concatenate(s,X2),inverse(k_ca)))
| ~ knows(sign(concatenate(X0,concatenate(n,X1)),inverse(first(X2)))) ),
inference(superposition,[status(thm)],[c_53,c_2601]) ).
tcf(c_2679,plain,
! [X0: $i,X1: $i,X2: $i] :
( knows(symmetric_encrypt(secret,X0))
| ~ knows(sign(concatenate(X0,concatenate(n,X1)),inverse(first(X2))))
| ~ knows(sign(concatenate(s,X2),inverse(k_ca))) ),
inference(global_subsumption_just,[status(thm)],[c_2605,c_518,c_2605]) ).
tcf(c_2680,plain,
! [X0: $i,X1: $i,X2: $i] :
( knows(symmetric_encrypt(secret,X0))
| ~ knows(sign(concatenate(s,X2),inverse(k_ca)))
| ~ knows(sign(concatenate(X0,concatenate(n,X1)),inverse(first(X2)))) ),
inference(renaming,[status(thm)],[c_2679]) ).
tcf(c_2686,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( knows(symmetric_encrypt(secret,X0))
| ~ knows(sign(concatenate(s,concatenate(X2,X3)),inverse(k_ca)))
| ~ knows(sign(concatenate(X0,concatenate(n,X1)),inverse(X2))) ),
inference(superposition,[status(thm)],[c_67,c_2680]) ).
tcf(c_2717,plain,
! [X0: $i,X1: $i] :
( knows(symmetric_encrypt(secret,X0))
| ~ knows(sign(concatenate(X0,concatenate(n,X1)),inverse(k_s))) ),
inference(superposition,[status(thm)],[c_1455,c_2686]) ).
tcf(c_2789,plain,
! [X0: $i] :
( iPr_def_10(X0)
| knows(symmetric_encrypt(secret,kgen(X0)))
| ~ knows(n)
| ~ knows(X0)
| ~ knows(inverse(X0)) ),
inference(superposition,[status(thm)],[c_595,c_2717]) ).
tcf(c_2800,plain,
! [X0: $i] :
( knows(symmetric_encrypt(secret,kgen(X0)))
| ~ knows(n)
| ~ knows(X0)
| ~ knows(inverse(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2789,c_2592]) ).
tcf(c_2967,plain,
! [X0: $i] :
( knows(symmetric_encrypt(secret,kgen(X0)))
| ~ knows(inverse(X0))
| ~ knows(X0) ),
inference(global_subsumption_just,[status(thm)],[c_2800,c_382,c_2800]) ).
tcf(c_2968,plain,
! [X0: $i] :
( knows(symmetric_encrypt(secret,kgen(X0)))
| ~ knows(X0)
| ~ knows(inverse(X0)) ),
inference(renaming,[status(thm)],[c_2967]) ).
tcf(c_2973,plain,
! [X0: $i] :
( knows(secret)
| ~ knows(X0)
| ~ knows(kgen(X0))
| ~ knows(inverse(X0)) ),
inference(superposition,[status(thm)],[c_2968,c_50]) ).
tcf(c_3055,plain,
! [X0: $i,X1: $i] :
( ~ knows(X1)
| ~ knows(X0)
| ~ knows(inverse(X0)) ),
inference(global_subsumption_just,[status(thm)],[c_1973,c_72,c_76,c_518,c_1515,c_2277,c_2308,c_2518,c_2973]) ).
tcf(c_3061,plain,
! [X0: $i] :
( ~ knows(k_a)
| ~ knows(X0) ),
inference(superposition,[status(thm)],[c_71,c_3055]) ).
tcf(c_3064,plain,
( ~ knows(k_c)
| ~ knows(k_a) ),
inference(instantiation,[status(thm)],[c_3061]) ).
tcf(c_3065,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3064,c_518,c_72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV233+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 18:46:39 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 0.85/1.29 % SZS status Started for theBenchmark.p
% 0.85/1.29 % SZS status Theorem for theBenchmark.p
% 0.85/1.29
% 0.85/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.85/1.29
% 0.85/1.29 % ------ iProver source info
% 0.85/1.29
% 0.85/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.85/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.85/1.29 % git: non_committed_changes: false
% 0.85/1.29
% 0.85/1.29 % ------ Parsing...
% 0.85/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.85/1.29
% 0.85/1.29 % ------ Preprocessing... sup_sim: 0 pe_s pe_e %
% 0.85/1.29
% 0.85/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 1 0s scvd_e snvd_s sp: 0 0s snvd_e %
% 0.85/1.29
% 0.85/1.29 % ------ Preprocessing...
% 0.85/1.29 % ------ Proving...
% 0.85/1.29 % ------ Problem Properties
% 0.85/1.29
% 0.85/1.29 %
% 0.85/1.29 % clauses 32
% 0.85/1.29 % conjectures 1
% 0.85/1.29 % EPR 3
% 0.85/1.29 % Horn 31
% 0.85/1.29 % unary 10
% 0.85/1.29 % binary 8
% 0.85/1.29 % lits 71
% 0.85/1.29 % lits eq 8
% 0.85/1.29 % fd_pure 0
% 0.85/1.29 % fd_pseudo 0
% 0.85/1.29 % fd_cond 0
% 0.85/1.29 % fd_pseudo_cond 0
% 0.85/1.29 % AC symbols 0
% 0.85/1.29
% 0.85/1.29 % ------ Input Options Time Limit: Unbounded
% 0.85/1.29
% 0.85/1.29
% 0.85/1.29 % ------
% 0.85/1.29 % Current options:
% 0.85/1.29 % ------
% 0.85/1.29
% 0.85/1.29
% 0.85/1.29 %
% 0.85/1.29
% 0.85/1.29 % ------ Proving...
% 0.85/1.29 %
% 0.85/1.29
% 0.85/1.29 % SZS status Theorem for theBenchmark.p
% 0.85/1.29
% 0.85/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.85/1.29
% 0.85/1.29
%------------------------------------------------------------------------------