%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV300-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /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 : Wed Oct 7 10:57:01 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.25s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 15
% Syntax : Number of formulae : 103 ( 69 unt; 0 typ; 0 def)
% Number of atoms : 456 ( 118 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1404 ( 88 ~; 117 |; 0 &;1199 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 18 con; 0-3 aty)
% Number of variables : 229 ( 0 ^; 229 !; 0 ?; 229 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Event_Obad,type,
c_Event_Obad: $i ).
thf(tp_c_Event_Oevent_OSays,type,
c_Event_Oevent_OSays: $i > $i > $i > $i ).
thf(tp_c_Event_Oknows,type,
c_Event_Oknows: $i > $i > $i ).
thf(tp_c_List_Oset,type,
c_List_Oset: $i > $i > $i ).
thf(tp_c_Message_Oagent_OSpy,type,
c_Message_Oagent_OSpy: $i ).
thf(tp_c_Message_Oanalz,type,
c_Message_Oanalz: $i > $i ).
thf(tp_c_Message_Omsg_OCrypt,type,
c_Message_Omsg_OCrypt: $i > $i > $i ).
thf(tp_c_Message_Omsg_OKey,type,
c_Message_Omsg_OKey: $i > $i ).
thf(tp_c_Message_Omsg_OMPair,type,
c_Message_Omsg_OMPair: $i > $i > $i ).
thf(tp_c_Message_Omsg_ONonce,type,
c_Message_Omsg_ONonce: $i > $i ).
thf(tp_c_Message_Oparts,type,
c_Message_Oparts: $i > $i ).
thf(tp_c_Message_Osynth,type,
c_Message_Osynth: $i > $i ).
thf(tp_c_OtwayRees_Ootway,type,
c_OtwayRees_Ootway: $i ).
thf(tp_c_Public_OshrK,type,
c_Public_OshrK: $i > $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_c_insert,type,
c_insert: $i > $i > $i > $i ).
thf(tp_c_union,type,
c_union: $i > $i > $i > $i ).
thf(tp_tc_Event_Oevent,type,
tc_Event_Oevent: $i ).
thf(tp_tc_List_Olist,type,
tc_List_Olist: $i > $i ).
thf(tp_tc_Message_Oagent,type,
tc_Message_Oagent: $i ).
thf(tp_tc_Message_Omsg,type,
tc_Message_Omsg: $i ).
thf(tp_v_A,type,
v_A: $i ).
thf(tp_v_Aaa,type,
v_Aaa: $i ).
thf(tp_v_Ba,type,
v_Ba: $i ).
thf(tp_v_K,type,
v_K: $i ).
thf(tp_v_Ka,type,
v_Ka: $i ).
thf(tp_v_NA,type,
v_NA: $i ).
thf(tp_v_NAa,type,
v_NAa: $i ).
thf(tp_v_NB,type,
v_NB: $i ).
thf(tp_v_X,type,
v_X: $i ).
thf(tp_v_evs4,type,
v_evs4: $i ).
thf(1,axiom,
! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a )
| ( c_in @ V_c @ V_B @ T_a )
| ( c_in @ V_c @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnE_0) ).
thf(2,axiom,
! [V_evs: $i,V_A: $i] :
( ~ ( c_in @ V_evs @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ V_A ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) ) @ tc_Message_Omsg )
| ( c_in @ V_A @ c_Event_Obad @ tc_Message_Oagent ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_OtwayRees_OSpy__see__shrK__D__dest_0) ).
thf(3,axiom,
! [V_X: $i,V_H: $i] :
( ~ ( c_in @ V_X @ V_H @ tc_Message_Omsg )
| ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Osynth_OInj_0) ).
thf(4,axiom,
! [V_c: $i,V_H: $i] :
( ~ ( c_in @ V_c @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
| ( c_in @ V_c @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__into__parts__dest_0) ).
thf(5,axiom,
! [V_X: $i,V_Y: $i,V_H: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ V_H ) ) @ tc_Message_Omsg )
| ( c_in @ V_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ V_H ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__synth__analz__iff1_0) ).
thf(6,axiom,
! [V_X: $i,V_Y: $i,V_H: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
| ( c_in @ V_Y @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).
thf(7,axiom,
! [V_Z: $i,V_X: $i,V_H: $i] :
( ~ ( c_in @ V_Z @ ( c_Message_Oparts @ ( c_insert @ V_X @ V_H @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_in @ V_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ V_H ) ) @ tc_Message_Omsg )
| ( c_in @ V_Z @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ V_H ) ) @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OFake__parts__insert__in__Un__dest_0) ).
thf(8,axiom,
! [V_K: $i,V_X: $i,V_H: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ V_H @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ V_K ) @ V_H @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_0) ).
thf(9,axiom,
! [V_A: $i,V_B: $i,V_X: $i,V_evs: $i] :
( ~ ( c_in @ ( c_Event_Oevent_OSays @ V_A @ V_B @ V_X ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ V_X @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OSays__imp__analz__Spy__dest_0) ).
thf(10,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(11,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[10]) ).
thf(12,negated_conjecture,
c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_insert @ v_X @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs4 ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).
thf(13,negated_conjecture,
~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs4 ) ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(14,negated_conjecture,
c_in @ ( c_Event_Oevent_OSays @ v_Aaa @ v_Ba @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_OMPair @ v_X @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_Ba ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Omsg_OKey @ v_Ka ) ) ) ) ) ) @ ( c_List_Oset @ v_evs4 @ tc_Event_Oevent ) @ tc_Event_Oevent,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(15,negated_conjecture,
c_in @ v_evs4 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(16,negated_conjecture,
~ ( c_in @ v_A @ c_Event_Obad @ tc_Message_Oagent ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(17,plain,
$false = $false,
inference(unfold_def,[status(thm)],[11]) ).
thf(18,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a )
| ( c_in @ V_c @ V_B @ T_a )
| ( c_in @ V_c @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(19,plain,
( ( ! [V_evs: $i,V_A: $i] :
( ~ ( c_in @ V_evs @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ V_A ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) ) @ tc_Message_Omsg )
| ( c_in @ V_A @ c_Event_Obad @ tc_Message_Oagent ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(20,plain,
( ( ! [V_X: $i,V_H: $i] :
( ~ ( c_in @ V_X @ V_H @ tc_Message_Omsg )
| ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(21,plain,
( ( ! [V_c: $i,V_H: $i] :
( ~ ( c_in @ V_c @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
| ( c_in @ V_c @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(22,plain,
( ( ! [V_X: $i,V_Y: $i,V_H: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ V_H ) ) @ tc_Message_Omsg )
| ( c_in @ V_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ V_H ) ) @ tc_Message_Omsg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(23,plain,
( ( ! [V_X: $i,V_Y: $i,V_H: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
| ( c_in @ V_Y @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(24,plain,
( ( ! [V_Z: $i,V_X: $i,V_H: $i] :
( ~ ( c_in @ V_Z @ ( c_Message_Oparts @ ( c_insert @ V_X @ V_H @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_in @ V_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ V_H ) ) @ tc_Message_Omsg )
| ( c_in @ V_Z @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ V_H ) ) @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(25,plain,
( ( ! [V_K: $i,V_X: $i,V_H: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ V_H @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ V_K ) @ V_H @ tc_Message_Omsg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(26,plain,
( ( ! [V_A: $i,V_B: $i,V_X: $i,V_evs: $i] :
( ~ ( c_in @ ( c_Event_Oevent_OSays @ V_A @ V_B @ V_X ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ V_X @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) ) @ tc_Message_Omsg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(27,plain,
( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_insert @ v_X @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs4 ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(28,plain,
( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs4 ) ) @ tc_Message_Omsg ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(29,plain,
( ( c_in @ ( c_Event_Oevent_OSays @ v_Aaa @ v_Ba @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_OMPair @ v_X @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_Ba ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Omsg_OKey @ v_Ka ) ) ) ) ) ) @ ( c_List_Oset @ v_evs4 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(30,plain,
( ( c_in @ v_evs4 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(31,plain,
( ( ~ ( c_in @ v_A @ c_Event_Obad @ tc_Message_Oagent ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(32,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(33,plain,
( ( ! [V_evs: $i] :
( ~ ( c_in @ V_evs @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ! [V_A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ V_A ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) ) @ tc_Message_Omsg )
| ( c_in @ V_A @ c_Event_Obad @ tc_Message_Oagent ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(34,plain,
( ( ~ ( c_in @ v_A @ c_Event_Obad @ tc_Message_Oagent ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(35,plain,
( ( c_in @ v_evs4 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(36,plain,
( ( c_in @ ( c_Event_Oevent_OSays @ v_Aaa @ v_Ba @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NAa ) @ ( c_Message_Omsg_OMPair @ v_X @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_Ba ) @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Omsg_OKey @ v_Ka ) ) ) ) ) ) @ ( c_List_Oset @ v_evs4 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(37,plain,
( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs4 ) ) @ tc_Message_Omsg ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(38,plain,
( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_insert @ v_X @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs4 ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(39,plain,
( ( ! [V_A: $i,V_B: $i,V_X: $i,V_evs: $i] :
( ~ ( c_in @ ( c_Event_Oevent_OSays @ V_A @ V_B @ V_X ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ V_X @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) ) @ tc_Message_Omsg ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(40,plain,
( ( ! [V_K: $i,V_X: $i,V_H: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ V_K @ V_X ) @ V_H @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ V_K ) @ V_H @ tc_Message_Omsg ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(41,plain,
( ( ! [V_Z: $i,V_X: $i,V_H: $i] :
( ~ ( c_in @ V_Z @ ( c_Message_Oparts @ ( c_insert @ V_X @ V_H @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_in @ V_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ V_H ) ) @ tc_Message_Omsg )
| ( c_in @ V_Z @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ V_H ) ) @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(42,plain,
( ( ! [V_X: $i,V_Y: $i,V_H: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
| ( c_in @ V_Y @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg ) ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(43,plain,
( ( ! [V_X: $i,V_Y: $i,V_H: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ V_X @ V_Y ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ V_H ) ) @ tc_Message_Omsg )
| ( c_in @ V_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ V_H ) ) @ tc_Message_Omsg ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(44,plain,
( ( ! [V_c: $i,V_H: $i] :
( ~ ( c_in @ V_c @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
| ( c_in @ V_c @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(45,plain,
( ( ! [V_X: $i,V_H: $i] :
( ~ ( c_in @ V_X @ V_H @ tc_Message_Omsg )
| ( c_in @ V_X @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(46,plain,
( ( ! [V_evs: $i] :
( ~ ( c_in @ V_evs @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ! [V_A: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ V_A ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) ) @ tc_Message_Omsg )
| ( c_in @ V_A @ c_Event_Obad @ tc_Message_Oagent ) ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(47,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a )
| ( c_in @ V_c @ V_B @ T_a )
| ( c_in @ V_c @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(48,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[32]) ).
thf(49,plain,
( ( c_in @ v_A @ c_Event_Obad @ tc_Message_Oagent )
= $false ),
inference(extcnf_not_pos,[status(thm)],[34]) ).
thf(50,plain,
( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs4 ) ) @ tc_Message_Omsg )
= $false ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(51,plain,
! [SV1: $i] :
( ( ! [SY26: $i,SY27: $i,SY28: $i] :
( ~ ( c_in @ ( c_Event_Oevent_OSays @ SV1 @ SY26 @ SY27 ) @ ( c_List_Oset @ SY28 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SY27 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SY28 ) ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[39]) ).
thf(52,plain,
! [SV2: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV2 @ SY29 ) @ ( c_Message_Osynth @ SY30 ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ SV2 @ SY29 ) @ SY30 @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ SV2 ) @ SY30 @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(53,plain,
! [SV3: $i] :
( ( ! [SY31: $i,SY32: $i] :
( ~ ( c_in @ SV3 @ ( c_Message_Oparts @ ( c_insert @ SY31 @ SY32 @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_in @ SY31 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SY32 ) ) @ tc_Message_Omsg )
| ( c_in @ SV3 @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SY32 ) ) @ ( c_Message_Oparts @ SY32 ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(54,plain,
! [SV4: $i] :
( ( ! [SY33: $i,SY34: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV4 @ SY33 ) @ ( c_Message_Oanalz @ SY34 ) @ tc_Message_Omsg )
| ( c_in @ SY33 @ ( c_Message_Oanalz @ SY34 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(55,plain,
! [SV5: $i] :
( ( ! [SY35: $i,SY36: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV5 @ SY35 ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SY36 ) ) @ tc_Message_Omsg )
| ( c_in @ SV5 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SY36 ) ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(56,plain,
! [SV6: $i] :
( ( ! [SY37: $i] :
( ~ ( c_in @ SV6 @ ( c_Message_Oanalz @ SY37 ) @ tc_Message_Omsg )
| ( c_in @ SV6 @ ( c_Message_Oparts @ SY37 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(57,plain,
! [SV7: $i] :
( ( ! [SY38: $i] :
( ~ ( c_in @ SV7 @ SY38 @ tc_Message_Omsg )
| ( c_in @ SV7 @ ( c_Message_Osynth @ SY38 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(58,plain,
! [SV8: $i] :
( ( ~ ( c_in @ SV8 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ! [SY39: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ SY39 ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
| ( c_in @ SY39 @ c_Event_Obad @ tc_Message_Oagent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(59,plain,
! [SV9: $i] :
( ( ! [SY40: $i,SY41: $i,SY42: $i] :
( ~ ( c_in @ SV9 @ ( c_union @ SY40 @ SY41 @ SY42 ) @ SY42 )
| ( c_in @ SV9 @ SY41 @ SY42 )
| ( c_in @ SV9 @ SY40 @ SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(60,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[48]) ).
thf(61,plain,
! [SV10: $i,SV1: $i] :
( ( ! [SY43: $i,SY44: $i] :
( ~ ( c_in @ ( c_Event_Oevent_OSays @ SV1 @ SV10 @ SY43 ) @ ( c_List_Oset @ SY44 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SY43 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SY44 ) ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(62,plain,
! [SV11: $i,SV2: $i] :
( ( ! [SY45: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV2 @ SV11 ) @ ( c_Message_Osynth @ SY45 ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ SV2 @ SV11 ) @ SY45 @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ SV2 ) @ SY45 @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(63,plain,
! [SV12: $i,SV3: $i] :
( ( ! [SY46: $i] :
( ~ ( c_in @ SV3 @ ( c_Message_Oparts @ ( c_insert @ SV12 @ SY46 @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_in @ SV12 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SY46 ) ) @ tc_Message_Omsg )
| ( c_in @ SV3 @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SY46 ) ) @ ( c_Message_Oparts @ SY46 ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(64,plain,
! [SV13: $i,SV4: $i] :
( ( ! [SY47: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV4 @ SV13 ) @ ( c_Message_Oanalz @ SY47 ) @ tc_Message_Omsg )
| ( c_in @ SV13 @ ( c_Message_Oanalz @ SY47 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(65,plain,
! [SV14: $i,SV5: $i] :
( ( ! [SY48: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV5 @ SV14 ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SY48 ) ) @ tc_Message_Omsg )
| ( c_in @ SV5 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SY48 ) ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(66,plain,
! [SV15: $i,SV6: $i] :
( ( ~ ( c_in @ SV6 @ ( c_Message_Oanalz @ SV15 ) @ tc_Message_Omsg )
| ( c_in @ SV6 @ ( c_Message_Oparts @ SV15 ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(67,plain,
! [SV16: $i,SV7: $i] :
( ( ~ ( c_in @ SV7 @ SV16 @ tc_Message_Omsg )
| ( c_in @ SV7 @ ( c_Message_Osynth @ SV16 ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(68,plain,
! [SV8: $i] :
( ( ( ~ ( c_in @ SV8 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
= $true )
| ( ( ! [SY39: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ SY39 ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
| ( c_in @ SY39 @ c_Event_Obad @ tc_Message_Oagent ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[58]) ).
thf(69,plain,
! [SV17: $i,SV9: $i] :
( ( ! [SY49: $i,SY50: $i] :
( ~ ( c_in @ SV9 @ ( c_union @ SV17 @ SY49 @ SY50 ) @ SY50 )
| ( c_in @ SV9 @ SY49 @ SY50 )
| ( c_in @ SV9 @ SV17 @ SY50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(70,plain,
! [SV18: $i,SV10: $i,SV1: $i] :
( ( ! [SY51: $i] :
( ~ ( c_in @ ( c_Event_Oevent_OSays @ SV1 @ SV10 @ SV18 ) @ ( c_List_Oset @ SY51 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV18 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SY51 ) ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(71,plain,
! [SV19: $i,SV11: $i,SV2: $i] :
( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV2 @ SV11 ) @ ( c_Message_Osynth @ SV19 ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ SV2 @ SV11 ) @ SV19 @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ SV2 ) @ SV19 @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(72,plain,
! [SV20: $i,SV12: $i,SV3: $i] :
( ( ~ ( c_in @ SV3 @ ( c_Message_Oparts @ ( c_insert @ SV12 @ SV20 @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_in @ SV12 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV20 ) ) @ tc_Message_Omsg )
| ( c_in @ SV3 @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV20 ) ) @ ( c_Message_Oparts @ SV20 ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(73,plain,
! [SV21: $i,SV13: $i,SV4: $i] :
( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV4 @ SV13 ) @ ( c_Message_Oanalz @ SV21 ) @ tc_Message_Omsg )
| ( c_in @ SV13 @ ( c_Message_Oanalz @ SV21 ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(74,plain,
! [SV22: $i,SV14: $i,SV5: $i] :
( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV5 @ SV14 ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV22 ) ) @ tc_Message_Omsg )
| ( c_in @ SV5 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV22 ) ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(75,plain,
! [SV15: $i,SV6: $i] :
( ( ( ~ ( c_in @ SV6 @ ( c_Message_Oanalz @ SV15 ) @ tc_Message_Omsg ) )
= $true )
| ( ( c_in @ SV6 @ ( c_Message_Oparts @ SV15 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(76,plain,
! [SV16: $i,SV7: $i] :
( ( ( ~ ( c_in @ SV7 @ SV16 @ tc_Message_Omsg ) )
= $true )
| ( ( c_in @ SV7 @ ( c_Message_Osynth @ SV16 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[67]) ).
thf(77,plain,
! [SV8: $i] :
( ( ( c_in @ SV8 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false )
| ( ( ! [SY39: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ SY39 ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
| ( c_in @ SY39 @ c_Event_Obad @ tc_Message_Oagent ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(78,plain,
! [SV23: $i,SV17: $i,SV9: $i] :
( ( ! [SY52: $i] :
( ~ ( c_in @ SV9 @ ( c_union @ SV17 @ SV23 @ SY52 ) @ SY52 )
| ( c_in @ SV9 @ SV23 @ SY52 )
| ( c_in @ SV9 @ SV17 @ SY52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(79,plain,
! [SV24: $i,SV18: $i,SV10: $i,SV1: $i] :
( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ SV1 @ SV10 @ SV18 ) @ ( c_List_Oset @ SV24 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV18 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV24 ) ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(80,plain,
! [SV19: $i,SV11: $i,SV2: $i] :
( ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV2 @ SV11 ) @ ( c_Message_Osynth @ SV19 ) @ tc_Message_Omsg ) )
= $true )
| ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV2 @ SV11 ) @ SV19 @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ SV2 ) @ SV19 @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(81,plain,
! [SV20: $i,SV12: $i,SV3: $i] :
( ( ( ~ ( c_in @ SV3 @ ( c_Message_Oparts @ ( c_insert @ SV12 @ SV20 @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
= $true )
| ( ( ~ ( c_in @ SV12 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV20 ) ) @ tc_Message_Omsg )
| ( c_in @ SV3 @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV20 ) ) @ ( c_Message_Oparts @ SV20 ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[72]) ).
thf(82,plain,
! [SV21: $i,SV13: $i,SV4: $i] :
( ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV4 @ SV13 ) @ ( c_Message_Oanalz @ SV21 ) @ tc_Message_Omsg ) )
= $true )
| ( ( c_in @ SV13 @ ( c_Message_Oanalz @ SV21 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[73]) ).
thf(83,plain,
! [SV22: $i,SV14: $i,SV5: $i] :
( ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV5 @ SV14 ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV22 ) ) @ tc_Message_Omsg ) )
= $true )
| ( ( c_in @ SV5 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV22 ) ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[74]) ).
thf(84,plain,
! [SV15: $i,SV6: $i] :
( ( ( c_in @ SV6 @ ( c_Message_Oanalz @ SV15 ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ SV6 @ ( c_Message_Oparts @ SV15 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[75]) ).
thf(85,plain,
! [SV16: $i,SV7: $i] :
( ( ( c_in @ SV7 @ SV16 @ tc_Message_Omsg )
= $false )
| ( ( c_in @ SV7 @ ( c_Message_Osynth @ SV16 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(86,plain,
! [SV8: $i,SV25: $i] :
( ( ( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ SV25 ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
| ( c_in @ SV25 @ c_Event_Obad @ tc_Message_Oagent ) )
= $true )
| ( ( c_in @ SV8 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(87,plain,
! [SV26: $i,SV23: $i,SV17: $i,SV9: $i] :
( ( ~ ( c_in @ SV9 @ ( c_union @ SV17 @ SV23 @ SV26 ) @ SV26 )
| ( c_in @ SV9 @ SV23 @ SV26 )
| ( c_in @ SV9 @ SV17 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(88,plain,
! [SV24: $i,SV18: $i,SV10: $i,SV1: $i] :
( ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ SV1 @ SV10 @ SV18 ) @ ( c_List_Oset @ SV24 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true )
| ( ( c_in @ SV18 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV24 ) ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[79]) ).
thf(89,plain,
! [SV19: $i,SV11: $i,SV2: $i] :
( ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV2 @ SV11 ) @ ( c_Message_Osynth @ SV19 ) @ tc_Message_Omsg )
= $false )
| ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV2 @ SV11 ) @ SV19 @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ SV2 ) @ SV19 @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(90,plain,
! [SV20: $i,SV12: $i,SV3: $i] :
( ( ( c_in @ SV3 @ ( c_Message_Oparts @ ( c_insert @ SV12 @ SV20 @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $false )
| ( ( ~ ( c_in @ SV12 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV20 ) ) @ tc_Message_Omsg )
| ( c_in @ SV3 @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV20 ) ) @ ( c_Message_Oparts @ SV20 ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(91,plain,
! [SV21: $i,SV13: $i,SV4: $i] :
( ( ( c_in @ ( c_Message_Omsg_OMPair @ SV4 @ SV13 ) @ ( c_Message_Oanalz @ SV21 ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ SV13 @ ( c_Message_Oanalz @ SV21 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(92,plain,
! [SV22: $i,SV14: $i,SV5: $i] :
( ( ( c_in @ ( c_Message_Omsg_OMPair @ SV5 @ SV14 ) @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV22 ) ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ SV5 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV22 ) ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[83]) ).
thf(93,plain,
! [SV8: $i,SV25: $i] :
( ( ( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ SV25 ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg ) )
= $true )
| ( ( c_in @ SV25 @ c_Event_Obad @ tc_Message_Oagent )
= $true )
| ( ( c_in @ SV8 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(94,plain,
! [SV26: $i,SV23: $i,SV17: $i,SV9: $i] :
( ( ( ~ ( c_in @ SV9 @ ( c_union @ SV17 @ SV23 @ SV26 ) @ SV26 ) )
= $true )
| ( ( ( c_in @ SV9 @ SV23 @ SV26 )
| ( c_in @ SV9 @ SV17 @ SV26 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(95,plain,
! [SV24: $i,SV18: $i,SV10: $i,SV1: $i] :
( ( ( c_in @ ( c_Event_Oevent_OSays @ SV1 @ SV10 @ SV18 ) @ ( c_List_Oset @ SV24 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( c_in @ SV18 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV24 ) ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(96,plain,
! [SV19: $i,SV11: $i,SV2: $i] :
( ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV2 @ SV11 ) @ SV19 @ tc_Message_Omsg )
= $true )
| ( ( c_in @ ( c_Message_Omsg_OKey @ SV2 ) @ SV19 @ tc_Message_Omsg )
= $true )
| ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV2 @ SV11 ) @ ( c_Message_Osynth @ SV19 ) @ tc_Message_Omsg )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(97,plain,
! [SV3: $i,SV20: $i,SV12: $i] :
( ( ( ~ ( c_in @ SV12 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV20 ) ) @ tc_Message_Omsg ) )
= $true )
| ( ( c_in @ SV3 @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV20 ) ) @ ( c_Message_Oparts @ SV20 ) @ tc_Message_Omsg ) @ tc_Message_Omsg )
= $true )
| ( ( c_in @ SV3 @ ( c_Message_Oparts @ ( c_insert @ SV12 @ SV20 @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[90]) ).
thf(98,plain,
! [SV8: $i,SV25: $i] :
( ( ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ SV25 ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV8 ) ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ SV25 @ c_Event_Obad @ tc_Message_Oagent )
= $true )
| ( ( c_in @ SV8 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[93]) ).
thf(99,plain,
! [SV26: $i,SV23: $i,SV17: $i,SV9: $i] :
( ( ( c_in @ SV9 @ ( c_union @ SV17 @ SV23 @ SV26 ) @ SV26 )
= $false )
| ( ( ( c_in @ SV9 @ SV23 @ SV26 )
| ( c_in @ SV9 @ SV17 @ SV26 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[94]) ).
thf(100,plain,
! [SV3: $i,SV20: $i,SV12: $i] :
( ( ( c_in @ SV12 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV20 ) ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ SV3 @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV20 ) ) @ ( c_Message_Oparts @ SV20 ) @ tc_Message_Omsg ) @ tc_Message_Omsg )
= $true )
| ( ( c_in @ SV3 @ ( c_Message_Oparts @ ( c_insert @ SV12 @ SV20 @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(101,plain,
! [SV17: $i,SV26: $i,SV23: $i,SV9: $i] :
( ( ( c_in @ SV9 @ SV23 @ SV26 )
= $true )
| ( ( c_in @ SV9 @ SV17 @ SV26 )
= $true )
| ( ( c_in @ SV9 @ ( c_union @ SV17 @ SV23 @ SV26 ) @ SV26 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[99]) ).
thf(102,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[35,101,100,98,96,95,92,91,85,84,60,50,49,38,36]) ).
thf(103,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[102]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV300-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.18 % Computer : n020.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 16:23:36 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.25
% 0.09/0.25 No.of.Axioms: 14
% 0.09/0.25
% 0.09/0.25 Length.of.Defs: 0
% 0.09/0.25
% 0.09/0.25 Contains.Choice.Funs: false
% 0.09/0.25 ...
% 0.09/0.25
% 0.09/0.25 ********************************
% 0.09/0.25 * All subproblems solved! *
% 0.09/0.25 ********************************
% 0.09/0.25 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:14,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:102,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 0.09/0.25
% 0.09/0.25 %**** Beginning of derivation protocol ****
% 0.09/0.25 % SZS output start CNFRefutation
% See solution above
% 0.09/0.25
% 0.09/0.25 %**** End of derivation protocol ****
% 0.09/0.25 %**** no. of clauses in derivation: 103 ****
% 0.09/0.25 %**** clause counter: 102 ****
% 0.09/0.25
% 0.09/0.25 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:14,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:102,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------