%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV314-2 : 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 : n019.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 10:57:14 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.27s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 46 ( 37 unt; 0 typ; 0 def)
% Number of atoms : 247 ( 58 equ; 0 cnn)
% Maximal formula atoms : 6 ( 5 avg)
% Number of connectives : 1210 ( 47 ~; 85 |; 0 &;1078 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 24 usr; 15 con; 0-3 aty)
% Number of variables : 102 ( 0 ^; 102 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Event_Obad,type,
c_Event_Obad: $i ).
thf(tp_c_Event_Oevent_ONotes,type,
c_Event_Oevent_ONotes: $i > $i > $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_OServer,type,
c_Message_Oagent_OServer: $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_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_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_B,type,
v_B: $i ).
thf(tp_v_K,type,
v_K: $i ).
thf(tp_v_NA,type,
v_NA: $i ).
thf(tp_v_NB,type,
v_NB: $i ).
thf(tp_v_evs,type,
v_evs: $i ).
thf(1,axiom,
! [V_evs: $i,V_B: $i,V_NA: $i,V_A: $i,V_K: $i,V_NB: $i] :
( ~ ( c_in @ V_evs @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ V_B @ ( c_Message_Omsg_OMPair @ V_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_A ) @ ( c_Message_Omsg_OMPair @ V_NA @ ( c_Message_Omsg_OKey @ V_K ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_B ) @ ( c_Message_Omsg_OMPair @ V_NB @ ( c_Message_Omsg_OKey @ V_K ) ) ) ) ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ V_K ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) ) @ tc_Message_Omsg )
| ( c_in @ V_B @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ V_A @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ V_NA @ ( c_Message_Omsg_OMPair @ V_NB @ ( c_Message_Omsg_OKey @ V_K ) ) ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_OtwayRees_Osecrecy__lemma__dest_0) ).
thf(2,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(3,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[2]) ).
thf(4,negated_conjecture,
c_in @ ( c_Message_Omsg_OKey @ v_K ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs ) ) @ tc_Message_Omsg,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(5,negated_conjecture,
c_in @ v_evs @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(6,negated_conjecture,
~ ( c_in @ v_B @ c_Event_Obad @ tc_Message_Oagent ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(7,negated_conjecture,
~ ( c_in @ v_A @ c_Event_Obad @ tc_Message_Oagent ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(8,negated_conjecture,
~ ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ v_NB @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) @ ( c_List_Oset @ v_evs @ tc_Event_Oevent ) @ tc_Event_Oevent ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(9,negated_conjecture,
c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_B @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ v_NB @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) ) ) @ ( c_List_Oset @ v_evs @ tc_Event_Oevent ) @ tc_Event_Oevent,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(10,plain,
$false = $false,
inference(unfold_def,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [V_evs: $i,V_B: $i,V_NA: $i,V_A: $i,V_K: $i,V_NB: $i] :
( ~ ( c_in @ V_evs @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ V_B @ ( c_Message_Omsg_OMPair @ V_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_A ) @ ( c_Message_Omsg_OMPair @ V_NA @ ( c_Message_Omsg_OKey @ V_K ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_B ) @ ( c_Message_Omsg_OMPair @ V_NB @ ( c_Message_Omsg_OKey @ V_K ) ) ) ) ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ V_K ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) ) @ tc_Message_Omsg )
| ( c_in @ V_B @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ V_A @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ V_NA @ ( c_Message_Omsg_OMPair @ V_NB @ ( c_Message_Omsg_OKey @ V_K ) ) ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(12,plain,
( ( c_in @ ( c_Message_Omsg_OKey @ v_K ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs ) ) @ tc_Message_Omsg )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(13,plain,
( ( c_in @ v_evs @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(14,plain,
( ( ~ ( c_in @ v_B @ c_Event_Obad @ tc_Message_Oagent ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(15,plain,
( ( ~ ( c_in @ v_A @ c_Event_Obad @ tc_Message_Oagent ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(16,plain,
( ( ~ ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ v_NB @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) @ ( c_List_Oset @ v_evs @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(17,plain,
( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_B @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ v_NB @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) ) ) @ ( c_List_Oset @ v_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(18,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(19,plain,
( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ v_B @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_A ) @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OKey @ v_K ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ v_B ) @ ( c_Message_Omsg_OMPair @ v_NB @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) ) ) @ ( c_List_Oset @ v_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $true ),
inference(copy,[status(thm)],[17]) ).
thf(20,plain,
( ( ~ ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ v_NB @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) @ ( c_List_Oset @ v_evs @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true ),
inference(copy,[status(thm)],[16]) ).
thf(21,plain,
( ( ~ ( c_in @ v_A @ c_Event_Obad @ tc_Message_Oagent ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(22,plain,
( ( ~ ( c_in @ v_B @ c_Event_Obad @ tc_Message_Oagent ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(23,plain,
( ( c_in @ v_evs @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(24,plain,
( ( c_in @ ( c_Message_Omsg_OKey @ v_K ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs ) ) @ tc_Message_Omsg )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(25,plain,
( ( ! [V_evs: $i,V_B: $i,V_NA: $i,V_A: $i,V_K: $i,V_NB: $i] :
( ~ ( c_in @ V_evs @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ V_B @ ( c_Message_Omsg_OMPair @ V_NA @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_A ) @ ( c_Message_Omsg_OMPair @ V_NA @ ( c_Message_Omsg_OKey @ V_K ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ V_B ) @ ( c_Message_Omsg_OMPair @ V_NB @ ( c_Message_Omsg_OKey @ V_K ) ) ) ) ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ V_K ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ V_evs ) ) @ tc_Message_Omsg )
| ( c_in @ V_B @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ V_A @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ V_NA @ ( c_Message_Omsg_OMPair @ V_NB @ ( c_Message_Omsg_OKey @ V_K ) ) ) ) @ ( c_List_Oset @ V_evs @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(26,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[18]) ).
thf(27,plain,
( ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ v_NA @ ( c_Message_Omsg_OMPair @ v_NB @ ( c_Message_Omsg_OKey @ v_K ) ) ) ) @ ( c_List_Oset @ v_evs @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false ),
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(28,plain,
( ( c_in @ v_A @ c_Event_Obad @ tc_Message_Oagent )
= $false ),
inference(extcnf_not_pos,[status(thm)],[21]) ).
thf(29,plain,
( ( c_in @ v_B @ c_Event_Obad @ tc_Message_Oagent )
= $false ),
inference(extcnf_not_pos,[status(thm)],[22]) ).
thf(30,plain,
! [SV1: $i] :
( ( ! [SY6: $i,SY7: $i,SY8: $i,SY9: $i,SY10: $i] :
( ~ ( c_in @ SV1 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SY6 @ ( c_Message_Omsg_OMPair @ SY7 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY8 ) @ ( c_Message_Omsg_OMPair @ SY7 @ ( c_Message_Omsg_OKey @ SY9 ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY6 ) @ ( c_Message_Omsg_OMPair @ SY10 @ ( c_Message_Omsg_OKey @ SY9 ) ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ SY9 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( c_in @ SY6 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ SY8 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ SY7 @ ( c_Message_Omsg_OMPair @ SY10 @ ( c_Message_Omsg_OKey @ SY9 ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(31,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[26]) ).
thf(32,plain,
! [SV2: $i,SV1: $i] :
( ( ! [SY11: $i,SY12: $i,SY13: $i,SY14: $i] :
( ~ ( c_in @ SV1 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV2 @ ( c_Message_Omsg_OMPair @ SY11 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY12 ) @ ( c_Message_Omsg_OMPair @ SY11 @ ( c_Message_Omsg_OKey @ SY13 ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV2 ) @ ( c_Message_Omsg_OMPair @ SY14 @ ( c_Message_Omsg_OKey @ SY13 ) ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ SY13 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( c_in @ SV2 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ SY12 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ SY11 @ ( c_Message_Omsg_OMPair @ SY14 @ ( c_Message_Omsg_OKey @ SY13 ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY15: $i,SY16: $i,SY17: $i] :
( ~ ( c_in @ SV1 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV2 @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SY15 ) @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OKey @ SY16 ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV2 ) @ ( c_Message_Omsg_OMPair @ SY17 @ ( c_Message_Omsg_OKey @ SY16 ) ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ SY16 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( c_in @ SV2 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ SY15 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ SY17 @ ( c_Message_Omsg_OKey @ SY16 ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(34,plain,
! [SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY18: $i,SY19: $i] :
( ~ ( c_in @ SV1 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV2 @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV4 ) @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OKey @ SY18 ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV2 ) @ ( c_Message_Omsg_OMPair @ SY19 @ ( c_Message_Omsg_OKey @ SY18 ) ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ SY18 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( c_in @ SV2 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ SV4 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ SY19 @ ( c_Message_Omsg_OKey @ SY18 ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[33]) ).
thf(35,plain,
! [SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ! [SY20: $i] :
( ~ ( c_in @ SV1 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV2 @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV4 ) @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV2 ) @ ( c_Message_Omsg_OMPair @ SY20 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ SV5 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( c_in @ SV2 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ SV4 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ SY20 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(36,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ~ ( c_in @ SV1 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV2 @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV4 ) @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV2 ) @ ( c_Message_Omsg_OMPair @ SV6 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ SV5 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( c_in @ SV2 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ SV4 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ SV6 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(37,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( ~ ( c_in @ SV1 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV2 @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV4 ) @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV2 ) @ ( c_Message_Omsg_OMPair @ SV6 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ SV5 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( c_in @ SV2 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ SV4 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ SV6 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[36]) ).
thf(38,plain,
! [SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i,SV1: $i] :
( ( ( c_in @ SV1 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false )
| ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV2 @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV4 ) @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV2 ) @ ( c_Message_Omsg_OMPair @ SV6 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ~ ( c_in @ ( c_Message_Omsg_OKey @ SV5 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( c_in @ SV2 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ SV4 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ SV6 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(39,plain,
! [SV1: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i] :
( ( ( ~ ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV2 @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV4 ) @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV2 ) @ ( c_Message_Omsg_OMPair @ SV6 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true )
| ( ( ~ ( c_in @ ( c_Message_Omsg_OKey @ SV5 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( c_in @ SV2 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ SV4 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ SV6 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true )
| ( ( c_in @ SV1 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(40,plain,
! [SV1: $i,SV6: $i,SV5: $i,SV4: $i,SV3: $i,SV2: $i] :
( ( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV2 @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV4 ) @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV2 ) @ ( c_Message_Omsg_OMPair @ SV6 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( ~ ( c_in @ ( c_Message_Omsg_OKey @ SV5 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
| ( c_in @ SV2 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ SV4 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ SV6 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true )
| ( ( c_in @ SV1 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(41,plain,
! [SV6: $i,SV3: $i,SV4: $i,SV2: $i,SV1: $i,SV5: $i] :
( ( ( ~ ( c_in @ ( c_Message_Omsg_OKey @ SV5 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg ) )
= $true )
| ( ( ( c_in @ SV2 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ SV4 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ SV6 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true )
| ( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV2 @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV4 ) @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV2 ) @ ( c_Message_Omsg_OMPair @ SV6 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( c_in @ SV1 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(42,plain,
! [SV6: $i,SV3: $i,SV4: $i,SV2: $i,SV1: $i,SV5: $i] :
( ( ( c_in @ ( c_Message_Omsg_OKey @ SV5 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
= $false )
| ( ( ( c_in @ SV2 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ SV4 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ SV6 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true )
| ( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV2 @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV4 ) @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV2 ) @ ( c_Message_Omsg_OMPair @ SV6 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( c_in @ SV1 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(43,plain,
! [SV1: $i,SV5: $i,SV6: $i,SV3: $i,SV4: $i,SV2: $i] :
( ( ( c_in @ SV2 @ c_Event_Obad @ tc_Message_Oagent )
= $true )
| ( ( ( c_in @ SV4 @ c_Event_Obad @ tc_Message_Oagent )
| ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ SV6 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true )
| ( ( c_in @ ( c_Message_Omsg_OKey @ SV5 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV2 @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV4 ) @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV2 ) @ ( c_Message_Omsg_OMPair @ SV6 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( c_in @ SV1 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[42]) ).
thf(44,plain,
! [SV2: $i,SV1: $i,SV5: $i,SV6: $i,SV3: $i,SV4: $i] :
( ( ( c_in @ SV4 @ c_Event_Obad @ tc_Message_Oagent )
= $true )
| ( ( c_in @ ( c_Event_Oevent_ONotes @ c_Message_Oagent_OSpy @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ SV6 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $true )
| ( ( c_in @ SV2 @ c_Event_Obad @ tc_Message_Oagent )
= $true )
| ( ( c_in @ ( c_Message_Omsg_OKey @ SV5 ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV1 ) ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ ( c_Event_Oevent_OSays @ c_Message_Oagent_OServer @ SV2 @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV4 ) @ ( c_Message_Omsg_OMPair @ SV3 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) @ ( c_Message_Omsg_OCrypt @ ( c_Public_OshrK @ SV2 ) @ ( c_Message_Omsg_OMPair @ SV6 @ ( c_Message_Omsg_OKey @ SV5 ) ) ) ) ) ) @ ( c_List_Oset @ SV1 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( c_in @ SV1 @ c_OtwayRees_Ootway @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[43]) ).
thf(45,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[19,44,31,29,28,27,24,23]) ).
thf(46,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV314-2 : 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
% 0.07/0.19 % Computer : n019.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 16:23:31 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.27
% 0.07/0.27 No.of.Axioms: 7
% 0.07/0.27
% 0.07/0.27 Length.of.Defs: 0
% 0.07/0.27
% 0.07/0.27 Contains.Choice.Funs: false
% 0.07/0.27 .
% 0.07/0.27
% 0.07/0.27 ********************************
% 0.07/0.27 * All subproblems solved! *
% 0.07/0.27 ********************************
% 0.07/0.27 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:7,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:45,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.27
% 0.07/0.27 %**** Beginning of derivation protocol ****
% 0.07/0.27 % SZS output start CNFRefutation
% See solution above
% 0.07/0.27
% 0.07/0.27 %**** End of derivation protocol ****
% 0.07/0.27 %**** no. of clauses in derivation: 46 ****
% 0.07/0.27 %**** clause counter: 45 ****
% 0.07/0.27
% 0.07/0.27 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:7,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:45,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------