%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV305-2 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 10:57:02 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.20s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 75 ( 50 unt; 0 typ; 0 def)
% Number of atoms : 338 ( 87 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1161 ( 65 ~; 89 |; 0 &;1007 @)
% ( 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 : 29 ( 26 usr; 15 con; 0-3 aty)
% Number of variables : 129 ( 0 ^; 129 !; 0 ?; 129 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Event_Obad,type,
c_Event_Obad: $i ).
thf(tp_c_Event_Oknows,type,
c_Event_Oknows: $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_OAgent,type,
c_Message_Omsg_OAgent: $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_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_A_H,type,
v_A_H: $i ).
thf(tp_v_B,type,
v_B: $i ).
thf(tp_v_NA,type,
v_NA: $i ).
thf(tp_v_NA_H,type,
v_NA_H: $i ).
thf(tp_v_X,type,
v_X: $i ).
thf(tp_v_evsf,type,
v_evsf: $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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_OtwayRees_OSpy__see__shrK__D__dest_0) ).
thf(3,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/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__into__parts__dest_0) ).
thf(4,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/sandbox2/benchmark/theBenchmark.p',cls_Message_OFake__parts__insert__in__Un__dest_0) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',cls_Message_OCrypt__synth_0) ).
thf(6,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(7,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[6]) ).
thf(8,negated_conjecture,
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA_H @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A_H ) @ ( c_Message_Omsg_OAgent @ v_A ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A ) @ ( c_Message_Omsg_OAgent @ v_B ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(9,negated_conjecture,
c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA_H @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A_H ) @ ( c_Message_Omsg_OAgent @ v_A ) ) ) ) ) @ ( c_Message_Oparts @ ( c_insert @ v_X @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(10,negated_conjecture,
c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A ) @ ( c_Message_Omsg_OAgent @ v_B ) ) ) ) @ ( c_Message_Oparts @ ( c_insert @ v_X @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(11,negated_conjecture,
c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) ) @ tc_Message_Omsg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(12,negated_conjecture,
c_in @ v_evsf @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(13,negated_conjecture,
~ ( c_in @ v_A @ c_Event_Obad @ tc_Message_Oagent ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(14,plain,
$false = $false,
inference(unfold_def,[status(thm)],[7]) ).
thf(15,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(16,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(17,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)],[3]) ).
thf(18,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)],[4]) ).
thf(19,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)],[5]) ).
thf(20,plain,
( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA_H @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A_H ) @ ( c_Message_Omsg_OAgent @ v_A ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A ) @ ( c_Message_Omsg_OAgent @ v_B ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) @ tc_Message_Omsg ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(21,plain,
( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA_H @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A_H ) @ ( c_Message_Omsg_OAgent @ v_A ) ) ) ) ) @ ( c_Message_Oparts @ ( c_insert @ v_X @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(22,plain,
( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A ) @ ( c_Message_Omsg_OAgent @ v_B ) ) ) ) @ ( c_Message_Oparts @ ( c_insert @ v_X @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(23,plain,
( ( c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) ) @ tc_Message_Omsg )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(24,plain,
( ( c_in @ v_evsf @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(25,plain,
( ( ~ ( c_in @ v_A @ c_Event_Obad @ tc_Message_Oagent ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(26,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[14]) ).
thf(27,plain,
( ( ~ ( c_in @ v_A @ c_Event_Obad @ tc_Message_Oagent ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(28,plain,
( ( c_in @ v_evsf @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(29,plain,
( ( c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) ) @ tc_Message_Omsg )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(30,plain,
( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A ) @ ( c_Message_Omsg_OAgent @ v_B ) ) ) ) @ ( c_Message_Oparts @ ( c_insert @ v_X @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(31,plain,
( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA_H @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A_H ) @ ( c_Message_Omsg_OAgent @ v_A ) ) ) ) ) @ ( c_Message_Oparts @ ( c_insert @ v_X @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(32,plain,
( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA_H @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A_H ) @ ( c_Message_Omsg_OAgent @ v_A ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) @ tc_Message_Omsg )
| ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A ) @ ( c_Message_Omsg_OAgent @ v_B ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) @ tc_Message_Omsg ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(33,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)],[19]) ).
thf(34,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)],[18]) ).
thf(35,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)],[17]) ).
thf(36,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(copy,[status(thm)],[16]) ).
thf(37,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)],[15]) ).
thf(38,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[26]) ).
thf(39,plain,
( ( c_in @ v_A @ c_Event_Obad @ tc_Message_Oagent )
= $false ),
inference(extcnf_not_pos,[status(thm)],[27]) ).
thf(40,plain,
( ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA_H @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A_H ) @ ( c_Message_Omsg_OAgent @ v_A ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) @ tc_Message_Omsg ) )
= $true )
| ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A ) @ ( c_Message_Omsg_OAgent @ v_B ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(41,plain,
! [SV1: $i] :
( ( ! [SY14: $i,SY15: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1 @ SY14 ) @ ( c_Message_Osynth @ SY15 ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ SV1 @ SY14 ) @ SY15 @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ SV1 ) @ SY15 @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(42,plain,
! [SV2: $i] :
( ( ! [SY16: $i,SY17: $i] :
( ~ ( c_in @ SV2 @ ( c_Message_Oparts @ ( c_insert @ SY16 @ SY17 @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_in @ SY16 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SY17 ) ) @ tc_Message_Omsg )
| ( c_in @ SV2 @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SY17 ) ) @ ( c_Message_Oparts @ SY17 ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(43,plain,
! [SV3: $i] :
( ( ! [SY18: $i] :
( ~ ( c_in @ SV3 @ ( c_Message_Oanalz @ SY18 ) @ tc_Message_Omsg )
| ( c_in @ SV3 @ ( c_Message_Oparts @ SY18 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(44,plain,
! [SV4: $i] :
( ( ! [SY19: $i] :
( ~ ( c_in @ SV4 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ SY19 ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV4 ) ) @ tc_Message_Omsg )
| ( c_in @ SY19 @ c_Event_Obad @ tc_Message_Oagent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(45,plain,
! [SV5: $i] :
( ( ! [SY20: $i,SY21: $i,SY22: $i] :
( ~ ( c_in @ SV5 @ ( c_union @ SY20 @ SY21 @ SY22 ) @ SY22 )
| ( c_in @ SV5 @ SY21 @ SY22 )
| ( c_in @ SV5 @ SY20 @ SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(46,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[38]) ).
thf(47,plain,
( ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA_H @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A_H ) @ ( c_Message_Omsg_OAgent @ v_A ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) @ tc_Message_Omsg )
= $false )
| ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A ) @ ( c_Message_Omsg_OAgent @ v_B ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[40]) ).
thf(48,plain,
! [SV6: $i,SV1: $i] :
( ( ! [SY23: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1 @ SV6 ) @ ( c_Message_Osynth @ SY23 ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ SV1 @ SV6 ) @ SY23 @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ SV1 ) @ SY23 @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(49,plain,
! [SV7: $i,SV2: $i] :
( ( ! [SY24: $i] :
( ~ ( c_in @ SV2 @ ( c_Message_Oparts @ ( c_insert @ SV7 @ SY24 @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_in @ SV7 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SY24 ) ) @ tc_Message_Omsg )
| ( c_in @ SV2 @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SY24 ) ) @ ( c_Message_Oparts @ SY24 ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(50,plain,
! [SV8: $i,SV3: $i] :
( ( ~ ( c_in @ SV3 @ ( c_Message_Oanalz @ SV8 ) @ tc_Message_Omsg )
| ( c_in @ SV3 @ ( c_Message_Oparts @ SV8 ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(51,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ( c_in @ SV4 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ SV9 ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV4 ) ) @ tc_Message_Omsg )
| ( c_in @ SV9 @ c_Event_Obad @ tc_Message_Oagent ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(52,plain,
! [SV10: $i,SV5: $i] :
( ( ! [SY25: $i,SY26: $i] :
( ~ ( c_in @ SV5 @ ( c_union @ SV10 @ SY25 @ SY26 ) @ SY26 )
| ( c_in @ SV5 @ SY25 @ SY26 )
| ( c_in @ SV5 @ SV10 @ SY26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(53,plain,
( ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A ) @ ( c_Message_Omsg_OAgent @ v_B ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA_H @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_A_H ) @ ( c_Message_Omsg_OAgent @ v_A ) ) ) ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evsf ) ) @ tc_Message_Omsg )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(54,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1 @ SV6 ) @ ( c_Message_Osynth @ SV11 ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OCrypt @ SV1 @ SV6 ) @ SV11 @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ SV1 ) @ SV11 @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(55,plain,
! [SV12: $i,SV7: $i,SV2: $i] :
( ( ~ ( c_in @ SV2 @ ( c_Message_Oparts @ ( c_insert @ SV7 @ SV12 @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_in @ SV7 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV12 ) ) @ tc_Message_Omsg )
| ( c_in @ SV2 @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV12 ) ) @ ( c_Message_Oparts @ SV12 ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(56,plain,
! [SV8: $i,SV3: $i] :
( ( ( ~ ( c_in @ SV3 @ ( c_Message_Oanalz @ SV8 ) @ tc_Message_Omsg ) )
= $true )
| ( ( c_in @ SV3 @ ( c_Message_Oparts @ SV8 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[50]) ).
thf(57,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( c_in @ SV4 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ SV9 ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV4 ) ) @ tc_Message_Omsg )
| ( c_in @ SV9 @ c_Event_Obad @ tc_Message_Oagent ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[51]) ).
thf(58,plain,
! [SV13: $i,SV10: $i,SV5: $i] :
( ( ! [SY27: $i] :
( ~ ( c_in @ SV5 @ ( c_union @ SV10 @ SV13 @ SY27 ) @ SY27 )
| ( c_in @ SV5 @ SV13 @ SY27 )
| ( c_in @ SV5 @ SV10 @ SY27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(59,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ( ~ ( c_in @ ( c_Message_Omsg_OCrypt @ SV1 @ SV6 ) @ ( c_Message_Osynth @ SV11 ) @ tc_Message_Omsg ) )
= $true )
| ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV1 @ SV6 ) @ SV11 @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ SV1 ) @ SV11 @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[54]) ).
thf(60,plain,
! [SV12: $i,SV7: $i,SV2: $i] :
( ( ( ~ ( c_in @ SV2 @ ( c_Message_Oparts @ ( c_insert @ SV7 @ SV12 @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
= $true )
| ( ( ~ ( c_in @ SV7 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV12 ) ) @ tc_Message_Omsg )
| ( c_in @ SV2 @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV12 ) ) @ ( c_Message_Oparts @ SV12 ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[55]) ).
thf(61,plain,
! [SV8: $i,SV3: $i] :
( ( ( c_in @ SV3 @ ( c_Message_Oanalz @ SV8 ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ SV3 @ ( c_Message_Oparts @ SV8 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[56]) ).
thf(62,plain,
! [SV9: $i,SV4: $i] :
( ( ( c_in @ SV4 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false )
| ( ( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ SV9 ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV4 ) ) @ tc_Message_Omsg )
| ( c_in @ SV9 @ c_Event_Obad @ tc_Message_Oagent ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[57]) ).
thf(63,plain,
! [SV14: $i,SV13: $i,SV10: $i,SV5: $i] :
( ( ~ ( c_in @ SV5 @ ( c_union @ SV10 @ SV13 @ SV14 ) @ SV14 )
| ( c_in @ SV5 @ SV13 @ SV14 )
| ( c_in @ SV5 @ SV10 @ SV14 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(64,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV1 @ SV6 ) @ ( c_Message_Osynth @ SV11 ) @ tc_Message_Omsg )
= $false )
| ( ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV1 @ SV6 ) @ SV11 @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_OKey @ SV1 ) @ SV11 @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(65,plain,
! [SV12: $i,SV7: $i,SV2: $i] :
( ( ( c_in @ SV2 @ ( c_Message_Oparts @ ( c_insert @ SV7 @ SV12 @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $false )
| ( ( ~ ( c_in @ SV7 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV12 ) ) @ tc_Message_Omsg )
| ( c_in @ SV2 @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV12 ) ) @ ( c_Message_Oparts @ SV12 ) @ tc_Message_Omsg ) @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[60]) ).
thf(66,plain,
! [SV4: $i,SV9: $i] :
( ( ( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ SV9 ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV4 ) ) @ tc_Message_Omsg ) )
= $true )
| ( ( c_in @ SV9 @ c_Event_Obad @ tc_Message_Oagent )
= $true )
| ( ( c_in @ SV4 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[62]) ).
thf(67,plain,
! [SV14: $i,SV13: $i,SV10: $i,SV5: $i] :
( ( ( ~ ( c_in @ SV5 @ ( c_union @ SV10 @ SV13 @ SV14 ) @ SV14 ) )
= $true )
| ( ( ( c_in @ SV5 @ SV13 @ SV14 )
| ( c_in @ SV5 @ SV10 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[63]) ).
thf(68,plain,
! [SV11: $i,SV6: $i,SV1: $i] :
( ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV1 @ SV6 ) @ SV11 @ tc_Message_Omsg )
= $true )
| ( ( c_in @ ( c_Message_Omsg_OKey @ SV1 ) @ SV11 @ tc_Message_Omsg )
= $true )
| ( ( c_in @ ( c_Message_Omsg_OCrypt @ SV1 @ SV6 ) @ ( c_Message_Osynth @ SV11 ) @ tc_Message_Omsg )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[64]) ).
thf(69,plain,
! [SV2: $i,SV12: $i,SV7: $i] :
( ( ( ~ ( c_in @ SV7 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV12 ) ) @ tc_Message_Omsg ) )
= $true )
| ( ( c_in @ SV2 @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV12 ) ) @ ( c_Message_Oparts @ SV12 ) @ tc_Message_Omsg ) @ tc_Message_Omsg )
= $true )
| ( ( c_in @ SV2 @ ( c_Message_Oparts @ ( c_insert @ SV7 @ SV12 @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[65]) ).
thf(70,plain,
! [SV4: $i,SV9: $i] :
( ( ( c_in @ ( c_Message_Omsg_OKey @ ( c_Public_OshrK @ SV9 ) ) @ ( c_Message_Oparts @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV4 ) ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ SV9 @ c_Event_Obad @ tc_Message_Oagent )
= $true )
| ( ( c_in @ SV4 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[66]) ).
thf(71,plain,
! [SV14: $i,SV13: $i,SV10: $i,SV5: $i] :
( ( ( c_in @ SV5 @ ( c_union @ SV10 @ SV13 @ SV14 ) @ SV14 )
= $false )
| ( ( ( c_in @ SV5 @ SV13 @ SV14 )
| ( c_in @ SV5 @ SV10 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(72,plain,
! [SV2: $i,SV12: $i,SV7: $i] :
( ( ( c_in @ SV7 @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV12 ) ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ SV2 @ ( c_union @ ( c_Message_Osynth @ ( c_Message_Oanalz @ SV12 ) ) @ ( c_Message_Oparts @ SV12 ) @ tc_Message_Omsg ) @ tc_Message_Omsg )
= $true )
| ( ( c_in @ SV2 @ ( c_Message_Oparts @ ( c_insert @ SV7 @ SV12 @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[69]) ).
thf(73,plain,
! [SV10: $i,SV14: $i,SV13: $i,SV5: $i] :
( ( ( c_in @ SV5 @ SV13 @ SV14 )
= $true )
| ( ( c_in @ SV5 @ SV10 @ SV14 )
= $true )
| ( ( c_in @ SV5 @ ( c_union @ SV10 @ SV13 @ SV14 ) @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(74,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,73,72,70,68,61,53,46,39,31,30,29]) ).
thf(75,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV305-2 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.14 % Computer : n010.cluster.edu
% 0.10/0.14 % Model : x86_64 x86_64
% 0.10/0.14 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.14 % Memory : 8046.5625MB
% 0.10/0.14 % OS : Linux 6.8.0-71-generic
% 0.10/0.14 % CPULimit : 300
% 0.10/0.14 % WCLimit : 300
% 0.10/0.14 % DateTime : Tue Oct 6 16:23:40 UTC 2026
% 0.10/0.15 % CPUTime :
% 0.10/0.15 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.20
% 0.10/0.20 No.of.Axioms: 11
% 0.10/0.20
% 0.10/0.20 Length.of.Defs: 0
% 0.10/0.20
% 0.10/0.20 Contains.Choice.Funs: false
% 0.10/0.20 .
% 0.10/0.20
% 0.10/0.20 ********************************
% 0.10/0.20 * All subproblems solved! *
% 0.10/0.20 ********************************
% 0.10/0.20 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:11,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:74,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.10/0.20
% 0.10/0.20 %**** Beginning of derivation protocol ****
% 0.10/0.20 % SZS output start CNFRefutation
% See solution above
% 0.10/0.20
% 0.10/0.20 %**** End of derivation protocol ****
% 0.10/0.20 %**** no. of clauses in derivation: 75 ****
% 0.10/0.20 %**** clause counter: 74 ****
% 0.10/0.20
% 0.10/0.20 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:11,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:74,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------