%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV281-2 : 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 : n026.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 10:56:55 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.18s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 49 ( 39 unt; 0 typ; 0 def)
% Number of atoms : 178 ( 86 equ; 0 cnn)
% Maximal formula atoms : 3 ( 3 avg)
% Number of connectives : 323 ( 30 ~; 31 |; 0 &; 262 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 95 ( 0 ^; 95 !; 0 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_0,type,
c_0: $i ).
thf(tp_c_Event_Oused,type,
c_Event_Oused: $i > $i ).
thf(tp_c_List_Olist_OCons,type,
c_List_Olist_OCons: $i > $i > $i > $i ).
thf(tp_c_List_Olist_ONil,type,
c_List_Olist_ONil: $i ).
thf(tp_c_Message_Omsg_ONonce,type,
c_Message_Omsg_ONonce: $i > $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_c_plus,type,
c_plus: $i > $i > $i > $i ).
thf(tp_tc_Message_Omsg,type,
tc_Message_Omsg: $i ).
thf(tp_tc_nat,type,
tc_nat: $i ).
thf(tp_v_evs,type,
v_evs: $i ).
thf(tp_v_evs_H,type,
v_evs_H: $i ).
thf(tp_v_sko__urX,type,
v_sko__urX: $i > $i ).
thf(1,axiom,
! [V_U: $i,V_evs: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ V_U ) @ ( c_Event_Oused @ V_evs ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ ( v_sko__urX @ V_evs ) @ V_U @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Public_ONonce__supply__lemma_0) ).
thf(2,axiom,
! [V_y: $i] :
( ( c_plus @ c_0 @ V_y @ tc_nat )
= V_y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Oop_A_L_Oadd__0_0) ).
thf(3,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_plus @ V_m @ V_k @ tc_nat )
!= ( c_plus @ V_n @ V_k @ tc_nat ) )
| ( V_m = V_n ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Onat__add__right__cancel_0) ).
thf(4,axiom,
! [V_n: $i,V_m: $i] : ( c_lessequals @ V_n @ ( c_plus @ V_m @ V_n @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nat_Ole__add2_0) ).
thf(5,axiom,
! [V_a_H: $i,V_list_H: $i,T_a: $i] :
( c_List_Olist_ONil
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_List_Olist_Odistinct__1_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,
! [V_U: $i,V_V: $i] :
( ( V_U = V_V )
| ( c_in @ ( c_Message_Omsg_ONonce @ V_V ) @ ( c_Event_Oused @ v_evs_H ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ V_U ) @ ( c_Event_Oused @ v_evs ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(9,plain,
$false = $false,
inference(unfold_def,[status(thm)],[7]) ).
thf(10,plain,
( ( ! [V_U: $i,V_evs: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ V_U ) @ ( c_Event_Oused @ V_evs ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ ( v_sko__urX @ V_evs ) @ V_U @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [V_y: $i] :
( ( c_plus @ c_0 @ V_y @ tc_nat )
= V_y ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_plus @ V_m @ V_k @ tc_nat )
!= ( c_plus @ V_n @ V_k @ tc_nat ) )
| ( V_m = V_n ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [V_n: $i,V_m: $i] : ( c_lessequals @ V_n @ ( c_plus @ V_m @ V_n @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(14,plain,
( ( ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
( c_List_Olist_ONil
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(15,plain,
( ( ! [V_U: $i,V_V: $i] :
( ( V_U = V_V )
| ( c_in @ ( c_Message_Omsg_ONonce @ V_V ) @ ( c_Event_Oused @ v_evs_H ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ V_U ) @ ( c_Event_Oused @ v_evs ) @ tc_Message_Omsg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(16,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [V_U: $i,V_V: $i] :
( ( V_U = V_V )
| ( c_in @ ( c_Message_Omsg_ONonce @ V_V ) @ ( c_Event_Oused @ v_evs_H ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ V_U ) @ ( c_Event_Oused @ v_evs ) @ tc_Message_Omsg ) ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(18,plain,
( ( ! [V_a_H: $i,V_list_H: $i,T_a: $i] :
( c_List_Olist_ONil
!= ( c_List_Olist_OCons @ V_a_H @ V_list_H @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(19,plain,
( ( ! [V_n: $i,V_m: $i] : ( c_lessequals @ V_n @ ( c_plus @ V_m @ V_n @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(20,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ( ( c_plus @ V_m @ V_k @ tc_nat )
!= ( c_plus @ V_n @ V_k @ tc_nat ) )
| ( V_m = V_n ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(21,plain,
( ( ! [V_y: $i] :
( ( c_plus @ c_0 @ V_y @ tc_nat )
= V_y ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(22,plain,
( ( ! [V_U: $i,V_evs: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ V_U ) @ ( c_Event_Oused @ V_evs ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ ( v_sko__urX @ V_evs ) @ V_U @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(23,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[16]) ).
thf(24,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( c_plus @ SX0 @ SX1 @ tc_nat )
!= ( c_plus @ SX2 @ SX1 @ tc_nat ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(25,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( c_List_Olist_ONil
!= ( c_List_Olist_OCons @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(26,plain,
! [SV1: $i] :
( ( ! [SY13: $i] :
( ( SV1 = SY13 )
| ( c_in @ ( c_Message_Omsg_ONonce @ SY13 ) @ ( c_Event_Oused @ v_evs_H ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ SV1 ) @ ( c_Event_Oused @ v_evs ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(27,plain,
! [SV2: $i] :
( ( ! [SY14: $i] : ( c_lessequals @ SV2 @ ( c_plus @ SY14 @ SV2 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(28,plain,
! [SV3: $i] :
( ( ( c_plus @ c_0 @ SV3 @ tc_nat )
= SV3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(29,plain,
! [SV4: $i] :
( ( ! [SY15: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ SV4 ) @ ( c_Event_Oused @ SY15 ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ ( v_sko__urX @ SY15 ) @ SV4 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[22]) ).
thf(30,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[23]) ).
thf(31,plain,
! [SV5: $i] :
( ( ! [SY16: $i,SY17: $i] :
( ( ( c_plus @ SV5 @ SY16 @ tc_nat )
!= ( c_plus @ SY17 @ SY16 @ tc_nat ) )
| ( SV5 = SY17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[24]) ).
thf(32,plain,
! [SV6: $i] :
( ( ! [SY18: $i,SY19: $i] :
( c_List_Olist_ONil
!= ( c_List_Olist_OCons @ SV6 @ SY18 @ SY19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[25]) ).
thf(33,plain,
! [SV7: $i,SV1: $i] :
( ( ( SV1 = SV7 )
| ( c_in @ ( c_Message_Omsg_ONonce @ SV7 ) @ ( c_Event_Oused @ v_evs_H ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ SV1 ) @ ( c_Event_Oused @ v_evs ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[26]) ).
thf(34,plain,
! [SV8: $i,SV2: $i] :
( ( c_lessequals @ SV2 @ ( c_plus @ SV8 @ SV2 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[27]) ).
thf(35,plain,
! [SV9: $i,SV4: $i] :
( ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ SV4 ) @ ( c_Event_Oused @ SV9 ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ ( v_sko__urX @ SV9 ) @ SV4 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV10: $i,SV5: $i] :
( ( ! [SY20: $i] :
( ( ( c_plus @ SV5 @ SV10 @ tc_nat )
!= ( c_plus @ SY20 @ SV10 @ tc_nat ) )
| ( SV5 = SY20 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[31]) ).
thf(37,plain,
! [SV11: $i,SV6: $i] :
( ( ! [SY21: $i] :
( c_List_Olist_ONil
!= ( c_List_Olist_OCons @ SV6 @ SV11 @ SY21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[32]) ).
thf(38,plain,
! [SV7: $i,SV1: $i] :
( ( ( SV1 = SV7 )
= $true )
| ( ( ( c_in @ ( c_Message_Omsg_ONonce @ SV7 ) @ ( c_Event_Oused @ v_evs_H ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ SV1 ) @ ( c_Event_Oused @ v_evs ) @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[33]) ).
thf(39,plain,
! [SV9: $i,SV4: $i] :
( ( ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ SV4 ) @ ( c_Event_Oused @ SV9 ) @ tc_Message_Omsg ) )
= $true )
| ( ( ~ ( c_lessequals @ ( v_sko__urX @ SV9 ) @ SV4 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV12: $i,SV10: $i,SV5: $i] :
( ( ( ( c_plus @ SV5 @ SV10 @ tc_nat )
!= ( c_plus @ SV12 @ SV10 @ tc_nat ) )
| ( SV5 = SV12 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV13: $i,SV11: $i,SV6: $i] :
( ( c_List_Olist_ONil
!= ( c_List_Olist_OCons @ SV6 @ SV11 @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV1: $i,SV7: $i] :
( ( ( c_in @ ( c_Message_Omsg_ONonce @ SV7 ) @ ( c_Event_Oused @ v_evs_H ) @ tc_Message_Omsg )
= $true )
| ( ( c_in @ ( c_Message_Omsg_ONonce @ SV1 ) @ ( c_Event_Oused @ v_evs ) @ tc_Message_Omsg )
= $true )
| ( ( SV1 = SV7 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV9: $i,SV4: $i] :
( ( ( c_in @ ( c_Message_Omsg_ONonce @ SV4 ) @ ( c_Event_Oused @ SV9 ) @ tc_Message_Omsg )
= $false )
| ( ( ~ ( c_lessequals @ ( v_sko__urX @ SV9 ) @ SV4 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV12: $i,SV10: $i,SV5: $i] :
( ( ( ( c_plus @ SV5 @ SV10 @ tc_nat )
!= ( c_plus @ SV12 @ SV10 @ tc_nat ) )
= $true )
| ( ( SV5 = SV12 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[40]) ).
thf(45,plain,
! [SV13: $i,SV11: $i,SV6: $i] :
( ( c_List_Olist_ONil
= ( c_List_Olist_OCons @ SV6 @ SV11 @ SV13 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[41]) ).
thf(46,plain,
! [SV4: $i,SV9: $i] :
( ( ( c_lessequals @ ( v_sko__urX @ SV9 ) @ SV4 @ tc_nat )
= $false )
| ( ( c_in @ ( c_Message_Omsg_ONonce @ SV4 ) @ ( c_Event_Oused @ SV9 ) @ tc_Message_Omsg )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(47,plain,
! [SV12: $i,SV10: $i,SV5: $i] :
( ( ( ( c_plus @ SV5 @ SV10 @ tc_nat )
= ( c_plus @ SV12 @ SV10 @ tc_nat ) )
= $false )
| ( ( SV5 = SV12 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[44]) ).
thf(48,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[28,47,46,45,42,34,30]) ).
thf(49,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[48]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV281-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.15 % Computer : n026.cluster.edu
% 0.09/0.15 % Model : x86_64 x86_64
% 0.09/0.15 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.15 % Memory : 8046.5625MB
% 0.09/0.15 % OS : Linux 6.8.0-71-generic
% 0.09/0.15 % CPULimit : 300
% 0.09/0.15 % WCLimit : 300
% 0.09/0.15 % DateTime : Tue Oct 6 16:25:32 UTC 2026
% 0.09/0.15 % CPUTime :
% 0.09/0.15 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.18
% 0.09/0.18 No.of.Axioms: 6
% 0.09/0.18
% 0.09/0.18 Length.of.Defs: 0
% 0.09/0.18
% 0.09/0.18 Contains.Choice.Funs: false
% 0.09/0.18 .
% 0.09/0.18
% 0.09/0.18 ********************************
% 0.09/0.18 * All subproblems solved! *
% 0.09/0.18 ********************************
% 0.09/0.18 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:6,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:48,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.09/0.18
% 0.09/0.18 %**** Beginning of derivation protocol ****
% 0.09/0.18 % SZS output start CNFRefutation
% See solution above
% 0.09/0.18
% 0.09/0.18 %**** End of derivation protocol ****
% 0.09/0.18 %**** no. of clauses in derivation: 49 ****
% 0.09/0.18 %**** clause counter: 48 ****
% 0.09/0.18
% 0.09/0.18 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:6,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:48,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------