%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV357-2 : 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 10:57:28 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.21s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 36 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 138 ( 37 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 379 ( 28 ~; 28 |; 0 &; 323 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 10 con; 0-3 aty)
% Number of variables : 54 ( 0 ^; 54 !; 0 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Event_Oevent_OGets,type,
c_Event_Oevent_OGets: $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_OAgent,type,
c_Message_Omsg_OAgent: $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_Yahalom_Oyahalom,type,
c_Yahalom_Oyahalom: $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_Omsg,type,
tc_Message_Omsg: $i ).
thf(tp_v_Aa,type,
v_Aa: $i ).
thf(tp_v_Ba,type,
v_Ba: $i ).
thf(tp_v_NB,type,
v_NB: $i ).
thf(tp_v_evs2,type,
v_evs2: $i ).
thf(1,axiom,
! [V_evs: $i,V_B: $i,V_X: $i] :
( ~ ( c_in @ V_evs @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ 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/sandbox2/benchmark/theBenchmark.p',cls_Yahalom_OGets__imp__analz__Spy__dest_0) ).
thf(2,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/sandbox2/benchmark/theBenchmark.p',cls_Message_OMPair__analz_0) ).
thf(3,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(4,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[3]) ).
thf(5,negated_conjecture,
~ ( c_in @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs2 ) ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(6,negated_conjecture,
c_in @ ( c_Event_Oevent_OGets @ v_Ba @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_ONonce @ v_NB ) ) ) @ ( c_List_Oset @ v_evs2 @ tc_Event_Oevent ) @ tc_Event_Oevent,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(7,negated_conjecture,
c_in @ v_evs2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(8,plain,
$false = $false,
inference(unfold_def,[status(thm)],[4]) ).
thf(9,plain,
( ( ! [V_evs: $i,V_B: $i,V_X: $i] :
( ~ ( c_in @ V_evs @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ 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)],[1]) ).
thf(10,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)],[2]) ).
thf(11,plain,
( ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs2 ) ) @ tc_Message_Omsg ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(12,plain,
( ( c_in @ ( c_Event_Oevent_OGets @ v_Ba @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_ONonce @ v_NB ) ) ) @ ( c_List_Oset @ v_evs2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(13,plain,
( ( c_in @ v_evs2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(14,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[8]) ).
thf(15,plain,
( ( c_in @ v_evs2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(16,plain,
( ( c_in @ ( c_Event_Oevent_OGets @ v_Ba @ ( c_Message_Omsg_OMPair @ ( c_Message_Omsg_OAgent @ v_Aa ) @ ( c_Message_Omsg_ONonce @ v_NB ) ) ) @ ( c_List_Oset @ v_evs2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(17,plain,
( ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs2 ) ) @ tc_Message_Omsg ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(18,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)],[10]) ).
thf(19,plain,
( ( ! [V_evs: $i,V_B: $i,V_X: $i] :
( ~ ( c_in @ V_evs @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ 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)],[9]) ).
thf(20,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[14]) ).
thf(21,plain,
( ( c_in @ ( c_Message_Omsg_ONonce @ v_NB ) @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ v_evs2 ) ) @ tc_Message_Omsg )
= $false ),
inference(extcnf_not_pos,[status(thm)],[17]) ).
thf(22,plain,
! [SV1: $i] :
( ( ! [SY6: $i,SY7: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1 @ SY6 ) @ ( c_Message_Oanalz @ SY7 ) @ tc_Message_Omsg )
| ( c_in @ SY6 @ ( c_Message_Oanalz @ SY7 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(23,plain,
! [SV2: $i] :
( ( ! [SY8: $i,SY9: $i] :
( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SY8 @ SY9 ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SY9 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(24,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[20]) ).
thf(25,plain,
! [SV3: $i,SV1: $i] :
( ( ! [SY10: $i] :
( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1 @ SV3 ) @ ( c_Message_Oanalz @ SY10 ) @ tc_Message_Omsg )
| ( c_in @ SV3 @ ( c_Message_Oanalz @ SY10 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(26,plain,
! [SV4: $i,SV2: $i] :
( ( ! [SY11: $i] :
( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV4 @ SY11 ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SY11 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[23]) ).
thf(27,plain,
! [SV5: $i,SV3: $i,SV1: $i] :
( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1 @ SV3 ) @ ( c_Message_Oanalz @ SV5 ) @ tc_Message_Omsg )
| ( c_in @ SV3 @ ( c_Message_Oanalz @ SV5 ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(28,plain,
! [SV6: $i,SV4: $i,SV2: $i] :
( ( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
| ~ ( c_in @ ( c_Event_Oevent_OGets @ SV4 @ SV6 ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV6 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(29,plain,
! [SV5: $i,SV3: $i,SV1: $i] :
( ( ( ~ ( c_in @ ( c_Message_Omsg_OMPair @ SV1 @ SV3 ) @ ( c_Message_Oanalz @ SV5 ) @ tc_Message_Omsg ) )
= $true )
| ( ( c_in @ SV3 @ ( c_Message_Oanalz @ SV5 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(30,plain,
! [SV6: $i,SV4: $i,SV2: $i] :
( ( ( ~ ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) ) )
= $true )
| ( ( ~ ( c_in @ ( c_Event_Oevent_OGets @ SV4 @ SV6 ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV6 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[28]) ).
thf(31,plain,
! [SV5: $i,SV3: $i,SV1: $i] :
( ( ( c_in @ ( c_Message_Omsg_OMPair @ SV1 @ SV3 ) @ ( c_Message_Oanalz @ SV5 ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ SV3 @ ( c_Message_Oanalz @ SV5 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[29]) ).
thf(32,plain,
! [SV6: $i,SV4: $i,SV2: $i] :
( ( ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false )
| ( ( ~ ( c_in @ ( c_Event_Oevent_OGets @ SV4 @ SV6 ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
| ( c_in @ SV6 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[30]) ).
thf(33,plain,
! [SV2: $i,SV6: $i,SV4: $i] :
( ( ( ~ ( c_in @ ( c_Event_Oevent_OGets @ SV4 @ SV6 ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent ) )
= $true )
| ( ( c_in @ SV6 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg )
= $true )
| ( ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[32]) ).
thf(34,plain,
! [SV2: $i,SV6: $i,SV4: $i] :
( ( ( c_in @ ( c_Event_Oevent_OGets @ SV4 @ SV6 ) @ ( c_List_Oset @ SV2 @ tc_Event_Oevent ) @ tc_Event_Oevent )
= $false )
| ( ( c_in @ SV6 @ ( c_Message_Oanalz @ ( c_Event_Oknows @ c_Message_Oagent_OSpy @ SV2 ) ) @ tc_Message_Omsg )
= $true )
| ( ( c_in @ SV2 @ c_Yahalom_Oyahalom @ ( tc_List_Olist @ tc_Event_Oevent ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[33]) ).
thf(35,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[15,34,31,24,21,16]) ).
thf(36,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[35]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV357-2 : 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
% 0.07/0.17 % Computer : n019.cluster.edu
% 0.07/0.17 % Model : x86_64 x86_64
% 0.07/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.17 % Memory : 8046.5625MB
% 0.07/0.17 % OS : Linux 6.8.0-71-generic
% 0.07/0.17 % CPULimit : 300
% 0.07/0.17 % WCLimit : 300
% 0.07/0.17 % DateTime : Tue Oct 6 16:26:46 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.21
% 0.07/0.21 No.of.Axioms: 5
% 0.07/0.21
% 0.07/0.21 Length.of.Defs: 0
% 0.07/0.21
% 0.07/0.21 Contains.Choice.Funs: false
% 0.07/0.21
% 0.07/0.21 ********************************
% 0.07/0.21 * All subproblems solved! *
% 0.07/0.21 ********************************
% 0.07/0.21 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:5,ps:0,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:35,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.21
% 0.07/0.21 %**** Beginning of derivation protocol ****
% 0.07/0.21 % SZS output start CNFRefutation
% See solution above
% 0.07/0.21
% 0.07/0.21 %**** End of derivation protocol ****
% 0.07/0.21 %**** no. of clauses in derivation: 36 ****
% 0.07/0.21 %**** clause counter: 35 ****
% 0.07/0.21
% 0.07/0.21 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:5,ps:0,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:35,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------