%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV255-2 : 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 10:56:40 AM UTC 2026
% Result : Unsatisfiable 0.07s 0.23s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 47 ( 31 unt; 0 typ; 0 def)
% Number of atoms : 182 ( 50 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 477 ( 38 ~; 35 |; 0 &; 404 @)
% ( 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 : 17 ( 14 usr; 9 con; 0-3 aty)
% Number of variables : 71 ( 0 ^; 71 !; 0 ?; 71 :)
% Comments :
%------------------------------------------------------------------------------
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_emptyset,type,
c_emptyset: $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_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_msg1,type,
v_msg1: $i ).
thf(tp_v_msg2,type,
v_msg2: $i ).
thf(tp_v_x,type,
v_x: $i ).
thf(tp_v_xa,type,
v_xa: $i ).
thf(tp_v_xb,type,
v_xb: $i > $i ).
thf(1,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ~ ( c_lessequals @ ( c_plus @ V_m @ V_k @ tc_nat ) @ V_n @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__leE_1) ).
thf(2,axiom,
! [V_m: $i,V_k: $i,V_n: $i] :
( ~ ( c_lessequals @ ( c_plus @ V_m @ V_k @ tc_nat ) @ V_n @ tc_nat )
| ( c_lessequals @ V_k @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__leE_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,
! [V_U: $i] :
( ( c_in @ ( c_Message_Omsg_ONonce @ ( v_xb @ V_U ) ) @ ( c_Message_Oparts @ ( c_insert @ v_msg2 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ ( v_xb @ V_U ) ) @ ( c_Message_Oparts @ ( c_insert @ v_msg1 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(6,negated_conjecture,
! [V_U: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ V_U ) @ ( c_Message_Oparts @ ( c_insert @ v_msg2 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ v_xa @ V_U @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(7,negated_conjecture,
! [V_U: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ V_U ) @ ( c_Message_Oparts @ ( c_insert @ v_msg1 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ v_x @ V_U @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(8,negated_conjecture,
! [V_U: $i] : ( c_lessequals @ V_U @ ( v_xb @ V_U ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(9,plain,
$false = $false,
inference(unfold_def,[status(thm)],[4]) ).
thf(10,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ~ ( c_lessequals @ ( c_plus @ V_m @ V_k @ tc_nat ) @ V_n @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(11,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ~ ( c_lessequals @ ( c_plus @ V_m @ V_k @ tc_nat ) @ V_n @ tc_nat )
| ( c_lessequals @ V_k @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(12,plain,
( ( ! [V_U: $i] :
( ( c_in @ ( c_Message_Omsg_ONonce @ ( v_xb @ V_U ) ) @ ( c_Message_Oparts @ ( c_insert @ v_msg2 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ ( v_xb @ V_U ) ) @ ( c_Message_Oparts @ ( c_insert @ v_msg1 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(13,plain,
( ( ! [V_U: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ V_U ) @ ( c_Message_Oparts @ ( c_insert @ v_msg2 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ v_xa @ V_U @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(14,plain,
( ( ! [V_U: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ V_U ) @ ( c_Message_Oparts @ ( c_insert @ v_msg1 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ v_x @ V_U @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(15,plain,
( ( ! [V_U: $i] : ( c_lessequals @ V_U @ ( v_xb @ V_U ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(16,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[9]) ).
thf(17,plain,
( ( ! [V_U: $i] : ( c_lessequals @ V_U @ ( v_xb @ V_U ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[15]) ).
thf(18,plain,
( ( ! [V_U: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ V_U ) @ ( c_Message_Oparts @ ( c_insert @ v_msg1 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ v_x @ V_U @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[14]) ).
thf(19,plain,
( ( ! [V_U: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ V_U ) @ ( c_Message_Oparts @ ( c_insert @ v_msg2 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ v_xa @ V_U @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[13]) ).
thf(20,plain,
( ( ! [V_U: $i] :
( ( c_in @ ( c_Message_Omsg_ONonce @ ( v_xb @ V_U ) ) @ ( c_Message_Oparts @ ( c_insert @ v_msg2 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ ( v_xb @ V_U ) ) @ ( c_Message_Oparts @ ( c_insert @ v_msg1 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) ) )
= $true ),
inference(copy,[status(thm)],[12]) ).
thf(21,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ~ ( c_lessequals @ ( c_plus @ V_m @ V_k @ tc_nat ) @ V_n @ tc_nat )
| ( c_lessequals @ V_k @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[11]) ).
thf(22,plain,
( ( ! [V_m: $i,V_k: $i,V_n: $i] :
( ~ ( c_lessequals @ ( c_plus @ V_m @ V_k @ tc_nat ) @ V_n @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[10]) ).
thf(23,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[16]) ).
thf(24,plain,
! [SV1: $i] :
( ( c_lessequals @ SV1 @ ( v_xb @ SV1 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[17]) ).
thf(25,plain,
! [SV2: $i] :
( ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ SV2 ) @ ( c_Message_Oparts @ ( c_insert @ v_msg1 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ v_x @ SV2 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[18]) ).
thf(26,plain,
! [SV3: $i] :
( ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ SV3 ) @ ( c_Message_Oparts @ ( c_insert @ v_msg2 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ v_xa @ SV3 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[19]) ).
thf(27,plain,
! [SV4: $i] :
( ( ( c_in @ ( c_Message_Omsg_ONonce @ ( v_xb @ SV4 ) ) @ ( c_Message_Oparts @ ( c_insert @ v_msg2 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ ( v_xb @ SV4 ) ) @ ( c_Message_Oparts @ ( c_insert @ v_msg1 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[20]) ).
thf(28,plain,
! [SV5: $i] :
( ( ! [SY10: $i,SY11: $i] :
( ~ ( c_lessequals @ ( c_plus @ SV5 @ SY10 @ tc_nat ) @ SY11 @ tc_nat )
| ( c_lessequals @ SY10 @ SY11 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[21]) ).
thf(29,plain,
! [SV6: $i] :
( ( ! [SY12: $i,SY13: $i] :
( ~ ( c_lessequals @ ( c_plus @ SV6 @ SY12 @ tc_nat ) @ SY13 @ tc_nat )
| ( c_lessequals @ SV6 @ SY13 @ 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,
! [SV2: $i] :
( ( ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ SV2 ) @ ( c_Message_Oparts @ ( c_insert @ v_msg1 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
= $true )
| ( ( ~ ( c_lessequals @ v_x @ SV2 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[25]) ).
thf(32,plain,
! [SV3: $i] :
( ( ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ SV3 ) @ ( c_Message_Oparts @ ( c_insert @ v_msg2 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg ) )
= $true )
| ( ( ~ ( c_lessequals @ v_xa @ SV3 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[26]) ).
thf(33,plain,
! [SV4: $i] :
( ( ( c_in @ ( c_Message_Omsg_ONonce @ ( v_xb @ SV4 ) ) @ ( c_Message_Oparts @ ( c_insert @ v_msg2 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $true )
| ( ( c_in @ ( c_Message_Omsg_ONonce @ ( v_xb @ SV4 ) ) @ ( c_Message_Oparts @ ( c_insert @ v_msg1 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[27]) ).
thf(34,plain,
! [SV7: $i,SV5: $i] :
( ( ! [SY14: $i] :
( ~ ( c_lessequals @ ( c_plus @ SV5 @ SV7 @ tc_nat ) @ SY14 @ tc_nat )
| ( c_lessequals @ SV7 @ SY14 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[28]) ).
thf(35,plain,
! [SV8: $i,SV6: $i] :
( ( ! [SY15: $i] :
( ~ ( c_lessequals @ ( c_plus @ SV6 @ SV8 @ tc_nat ) @ SY15 @ tc_nat )
| ( c_lessequals @ SV6 @ SY15 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[29]) ).
thf(36,plain,
! [SV2: $i] :
( ( ( c_in @ ( c_Message_Omsg_ONonce @ SV2 ) @ ( c_Message_Oparts @ ( c_insert @ v_msg1 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $false )
| ( ( ~ ( c_lessequals @ v_x @ SV2 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[31]) ).
thf(37,plain,
! [SV3: $i] :
( ( ( c_in @ ( c_Message_Omsg_ONonce @ SV3 ) @ ( c_Message_Oparts @ ( c_insert @ v_msg2 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $false )
| ( ( ~ ( c_lessequals @ v_xa @ SV3 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[32]) ).
thf(38,plain,
! [SV9: $i,SV7: $i,SV5: $i] :
( ( ~ ( c_lessequals @ ( c_plus @ SV5 @ SV7 @ tc_nat ) @ SV9 @ tc_nat )
| ( c_lessequals @ SV7 @ SV9 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[34]) ).
thf(39,plain,
! [SV10: $i,SV8: $i,SV6: $i] :
( ( ~ ( c_lessequals @ ( c_plus @ SV6 @ SV8 @ tc_nat ) @ SV10 @ tc_nat )
| ( c_lessequals @ SV6 @ SV10 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[35]) ).
thf(40,plain,
! [SV2: $i] :
( ( ( c_lessequals @ v_x @ SV2 @ tc_nat )
= $false )
| ( ( c_in @ ( c_Message_Omsg_ONonce @ SV2 ) @ ( c_Message_Oparts @ ( c_insert @ v_msg1 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[36]) ).
thf(41,plain,
! [SV3: $i] :
( ( ( c_lessequals @ v_xa @ SV3 @ tc_nat )
= $false )
| ( ( c_in @ ( c_Message_Omsg_ONonce @ SV3 ) @ ( c_Message_Oparts @ ( c_insert @ v_msg2 @ c_emptyset @ tc_Message_Omsg ) ) @ tc_Message_Omsg )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[37]) ).
thf(42,plain,
! [SV9: $i,SV7: $i,SV5: $i] :
( ( ( ~ ( c_lessequals @ ( c_plus @ SV5 @ SV7 @ tc_nat ) @ SV9 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV7 @ SV9 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[38]) ).
thf(43,plain,
! [SV10: $i,SV8: $i,SV6: $i] :
( ( ( ~ ( c_lessequals @ ( c_plus @ SV6 @ SV8 @ tc_nat ) @ SV10 @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV6 @ SV10 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[39]) ).
thf(44,plain,
! [SV9: $i,SV7: $i,SV5: $i] :
( ( ( c_lessequals @ ( c_plus @ SV5 @ SV7 @ tc_nat ) @ SV9 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV7 @ SV9 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[42]) ).
thf(45,plain,
! [SV10: $i,SV8: $i,SV6: $i] :
( ( ( c_lessequals @ ( c_plus @ SV6 @ SV8 @ tc_nat ) @ SV10 @ tc_nat )
= $false )
| ( ( c_lessequals @ SV6 @ SV10 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[43]) ).
thf(46,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[24,45,44,41,40,33,30]) ).
thf(47,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV255-2 : 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
% 0.07/0.18 % Computer : n020.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Oct 6 16:22:06 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.23
% 0.07/0.23 No.of.Axioms: 6
% 0.07/0.23
% 0.07/0.23 Length.of.Defs: 0
% 0.07/0.23
% 0.07/0.23 Contains.Choice.Funs: false
% 0.07/0.23
% 0.07/0.23 ********************************
% 0.07/0.23 * All subproblems solved! *
% 0.07/0.23 ********************************
% 0.07/0.23 % SZS status Unsatisfiable for /export/starexec/sandbox/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:46,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.07/0.23
% 0.07/0.23 %**** Beginning of derivation protocol ****
% 0.07/0.23 % SZS output start CNFRefutation
% See solution above
% 0.07/0.23
% 0.07/0.23 %**** End of derivation protocol ****
% 0.07/0.23 %**** no. of clauses in derivation: 47 ****
% 0.07/0.23 %**** clause counter: 46 ****
% 0.07/0.23
% 0.07/0.23 % SZS status Unsatisfiable for /export/starexec/sandbox/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:46,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------