%------------------------------------------------------------------------------
% File : Satallax---3.5
% Problem : ITP084^1 : TPTP v9.2.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Oct 9 01:46:55 PM UTC 2025
% Result : Theorem 28.95s 27.05s
% Output : Proof 28.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 13
% Syntax : Number of formulae : 41 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 125 ( 10 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 105 ( 33 ~; 27 |; 0 &; 42 @)
% ( 0 <=>; 1 =>; 2 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Number of types : 0 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 21 usr; 22 con; 0-2 aty)
% Number of variables : 4 ( 0 ^; 4 !; 0 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
thf(conj_0,conjecture,
knowle945212990e_know @ a @ ( secrecy_kKS @ m ) ).
thf(h0,negated_conjecture,
~ ( knowle945212990e_know @ a @ ( secrecy_kKS @ m ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
thf(ax1491,axiom,
( ~ p8
| p26 ),
file('<stdin>',ax1491) ).
thf(ax1461,axiom,
( ~ p26
| p57 ),
file('<stdin>',ax1461) ).
thf(ax1509,axiom,
p8,
file('<stdin>',ax1509) ).
thf(nax110,axiom,
( p110
<= ( fa = fa ) ),
file('<stdin>',nax110) ).
thf(ax1405,axiom,
( ~ p57
| ~ p104
| p21 ),
file('<stdin>',ax1405) ).
thf(ax1496,axiom,
~ p21,
file('<stdin>',ax1496) ).
thf(pax12,axiom,
( p12
=> ! [X286: secrecy_Keys] :
( ( fsecrec1016742679ession @ ( fsecrecy_kKS @ X286 ) )
= ( fsecrecy_kE @ X286 ) ) ),
file('<stdin>',pax12) ).
thf(ax1399,axiom,
( ~ p1
| p104
| ~ p110
| ~ p111 ),
file('<stdin>',ax1399) ).
thf(nax111,axiom,
( p111
<= ( ( fcons_S112077679ession @ ( fsecrecy_kE @ fm ) @ fnil_Se901661471ession )
= ( fcons_S112077679ession @ ( fsecrec1016742679ession @ ( fsecrecy_kKS @ fm ) ) @ fnil_Se901661471ession ) ) ),
file('<stdin>',nax111) ).
thf(ax1505,axiom,
p12,
file('<stdin>',ax1505) ).
thf(ax1516,axiom,
p1,
file('<stdin>',ax1516) ).
thf(c_0_11,plain,
( ~ p8
| p26 ),
inference(fof_simplification,[status(thm)],[ax1491]) ).
thf(c_0_12,plain,
( ~ p26
| p57 ),
inference(fof_simplification,[status(thm)],[ax1461]) ).
thf(c_0_13,plain,
( p26
| ~ p8 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
thf(c_0_14,plain,
p8,
inference(split_conjunct,[status(thm)],[ax1509]) ).
thf(c_0_15,plain,
( ( fa != fa )
| p110 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax110])]) ).
thf(c_0_16,plain,
( ~ p57
| ~ p104
| p21 ),
inference(fof_simplification,[status(thm)],[ax1405]) ).
thf(c_0_17,plain,
( p57
| ~ p26 ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
thf(c_0_18,plain,
p26,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]) ).
thf(c_0_19,plain,
~ p21,
inference(fof_simplification,[status(thm)],[ax1496]) ).
thf(c_0_20,plain,
! [X706: secrecy_Keys] :
( ~ p12
| ( ( fsecrec1016742679ession @ ( fsecrecy_kKS @ X706 ) )
= ( fsecrecy_kE @ X706 ) ) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[pax12])])]) ).
thf(c_0_21,plain,
( ~ p1
| p104
| ~ p110
| ~ p111 ),
inference(fof_simplification,[status(thm)],[ax1399]) ).
thf(c_0_22,plain,
( p110
| ( fa != fa ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
thf(c_0_23,plain,
( p21
| ~ p57
| ~ p104 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
thf(c_0_24,plain,
p57,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]) ).
thf(c_0_25,plain,
~ p21,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
thf(c_0_26,plain,
( ( ( fcons_S112077679ession @ ( fsecrecy_kE @ fm ) @ fnil_Se901661471ession )
!= ( fcons_S112077679ession @ ( fsecrec1016742679ession @ ( fsecrecy_kKS @ fm ) ) @ fnil_Se901661471ession ) )
| p111 ),
inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[nax111])]) ).
thf(c_0_27,plain,
! [X2: secrecy_Keys] :
( ( ( fsecrec1016742679ession @ ( fsecrecy_kKS @ X2 ) )
= ( fsecrecy_kE @ X2 ) )
| ~ p12 ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
thf(c_0_28,plain,
p12,
inference(split_conjunct,[status(thm)],[ax1505]) ).
thf(c_0_29,plain,
( p104
| ~ p1
| ~ p110
| ~ p111 ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
thf(c_0_30,plain,
p1,
inference(split_conjunct,[status(thm)],[ax1516]) ).
thf(c_0_31,plain,
p110,
inference(cn,[status(thm)],[c_0_22]) ).
thf(c_0_32,plain,
~ p104,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24])]),c_0_25]) ).
thf(c_0_33,plain,
( p111
| ( ( fcons_S112077679ession @ ( fsecrecy_kE @ fm ) @ fnil_Se901661471ession )
!= ( fcons_S112077679ession @ ( fsecrec1016742679ession @ ( fsecrecy_kKS @ fm ) ) @ fnil_Se901661471ession ) ) ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
thf(c_0_34,plain,
! [X2: secrecy_Keys] :
( ( fsecrec1016742679ession @ ( fsecrecy_kKS @ X2 ) )
= ( fsecrecy_kE @ X2 ) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]) ).
thf(c_0_35,plain,
~ p111,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),c_0_32]) ).
thf(c_0_36,plain,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_34])]),c_0_35]),
[proof] ).
thf(1,plain,
$false,
inference(eprover,[status(thm),assumptions([h0])],[]) ).
thf(0,theorem,
knowle945212990e_know @ a @ ( secrecy_kKS @ m ),
inference(contra,[status(thm),contra(discharge,[h0])],[1,h0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : ITP084^1 : TPTP v9.2.0. Released v7.5.0.
% 0.07/0.13 % Command : satallax -E eprover-ho -P picomus -M modes -p tstp -t %d %s
% 0.13/0.35 % Computer : n001.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Wed Oct 8 18:20:38 EDT 2025
% 0.13/0.35 % CPUTime :
% 28.95/27.05 % SZS status Theorem
% 28.95/27.05 % Mode: mode478:USE_SINE=true:SINE_TOLERANCE=2.0:SINE_GENERALITY_THRESHOLD=16:SINE_RANK_LIMIT=1.:SINE_DEPTH=0
% 28.95/27.05 % Inferences: 741
% 28.95/27.05 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------