%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SWV282-2 : 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 : n016.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 37.24s 6.46s
% Output : CNFRefutation 37.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 90 ( 70 unt; 0 typ; 0 def)
% Number of atoms : 379 ( 167 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 773 ( 40 ~; 91 |; 0 &; 642 @)
% ( 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 : 22 ( 19 usr; 9 con; 0-3 aty)
% Number of variables : 158 ( 0 ^; 158 !; 0 ?; 158 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_0,type,
c_0: $i ).
thf(tp_c_1,type,
c_1: $i ).
thf(tp_c_Binomial_Obinomial,type,
c_Binomial_Obinomial: $i > $i > $i ).
thf(tp_c_Event_Oused,type,
c_Event_Oused: $i > $i ).
thf(tp_c_Finite__Set_Ocard,type,
c_Finite__Set_Ocard: $i > $i > $i ).
thf(tp_c_Message_Omsg_ONonce,type,
c_Message_Omsg_ONonce: $i > $i ).
thf(tp_c_SetInterval_OatMost,type,
c_SetInterval_OatMost: $i > $i > $i ).
thf(tp_c_Suc,type,
c_Suc: $i > $i ).
thf(tp_c_in,type,
c_in: $i > $i > $i > $o ).
thf(tp_c_less,type,
c_less: $i > $i > $i > $o ).
thf(tp_c_lessequals,type,
c_lessequals: $i > $i > $i > $o ).
thf(tp_c_minus,type,
c_minus: $i > $i > $i > $i ).
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_evs_H_H,type,
v_evs_H_H: $i ).
thf(tp_v_sko__urX,type,
v_sko__urX: $i > $i ).
thf(1,axiom,
! [V_u: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatMost @ V_u @ tc_nat ) @ tc_nat )
= ( c_Suc @ V_u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SetInterval_Ocard__atMost_0) ).
thf(2,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/sandbox/benchmark/theBenchmark.p',cls_Public_ONonce__supply__lemma_0) ).
thf(3,axiom,
! [V_j: $i,V_i: $i] :
~ ( c_less @ ( c_plus @ V_j @ V_i @ tc_nat ) @ V_i @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onot__add__less2_0) ).
thf(4,axiom,
! [V_k: $i,V_m: $i,V_n: $i] :
( ~ ( c_lessequals @ ( c_plus @ V_k @ V_m @ tc_nat ) @ ( c_plus @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Onat__add__left__cancel__le_0) ).
thf(5,axiom,
! [V_m: $i,V_n: $i] :
( ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ( c_less @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oless__Suc__eq__le_1) ).
thf(6,axiom,
! [V_n: $i] : ( c_less @ V_n @ ( c_Suc @ V_n ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OlessI_0) ).
thf(7,axiom,
! [V_n: $i,V_m: $i] : ( c_lessequals @ V_n @ ( c_plus @ V_n @ V_m @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Ole__add1_0) ).
thf(8,axiom,
! [V_m: $i] :
( ( c_minus @ V_m @ V_m @ tc_nat )
= c_0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__self__eq__0_0) ).
thf(9,axiom,
! [V_m: $i,V_n: $i] :
( ( ( c_minus @ V_m @ V_n @ tc_nat )
!= c_0 )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__is__0__eq_0) ).
thf(10,axiom,
( c_1
= ( c_Suc @ c_0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_OOne__nat__def_0) ).
thf(11,axiom,
! [V_n: $i] :
( ( c_Binomial_Obinomial @ V_n @ c_0 )
= c_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__n__0_0) ).
thf(12,axiom,
! [V_n: $i,V_k: $i] :
( ( c_Binomial_Obinomial @ ( c_Suc @ V_n ) @ ( c_Suc @ V_k ) )
= ( c_plus @ ( c_Binomial_Obinomial @ V_n @ V_k ) @ ( c_Binomial_Obinomial @ V_n @ ( c_Suc @ V_k ) ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__Suc__Suc_0) ).
thf(13,axiom,
! [V_y: $i] :
( ( c_Binomial_Obinomial @ V_y @ ( c_Suc @ c_0 ) )
= V_y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Binomial_Obinomial__1_0) ).
thf(14,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(15,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[14]) ).
thf(16,negated_conjecture,
! [V_U: $i,V_W: $i,V_V: $i] :
( ( V_U = V_W )
| ( V_V = V_W )
| ( V_U = V_V )
| ( c_in @ ( c_Message_Omsg_ONonce @ V_W ) @ ( c_Event_Oused @ v_evs_H_H ) @ tc_Message_Omsg )
| ( 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/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(17,plain,
$false = $false,
inference(unfold_def,[status(thm)],[15]) ).
thf(18,plain,
( ( ! [V_u: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatMost @ V_u @ tc_nat ) @ tc_nat )
= ( c_Suc @ V_u ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(19,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)],[2]) ).
thf(20,plain,
( ( ! [V_j: $i,V_i: $i] :
~ ( c_less @ ( c_plus @ V_j @ V_i @ tc_nat ) @ V_i @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(21,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ~ ( c_lessequals @ ( c_plus @ V_k @ V_m @ tc_nat ) @ ( c_plus @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(22,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ( c_less @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(23,plain,
( ( ! [V_n: $i] : ( c_less @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(24,plain,
( ( ! [V_n: $i,V_m: $i] : ( c_lessequals @ V_n @ ( c_plus @ V_n @ V_m @ tc_nat ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(25,plain,
( ( ! [V_m: $i] :
( ( c_minus @ V_m @ V_m @ tc_nat )
= c_0 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(26,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_minus @ V_m @ V_n @ tc_nat )
!= c_0 )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(27,plain,
( ( c_1
= ( c_Suc @ c_0 ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(28,plain,
( ( ! [V_n: $i] :
( ( c_Binomial_Obinomial @ V_n @ c_0 )
= c_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(29,plain,
( ( ! [V_n: $i,V_k: $i] :
( ( c_Binomial_Obinomial @ ( c_Suc @ V_n ) @ ( c_Suc @ V_k ) )
= ( c_plus @ ( c_Binomial_Obinomial @ V_n @ V_k ) @ ( c_Binomial_Obinomial @ V_n @ ( c_Suc @ V_k ) ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(30,plain,
( ( ! [V_y: $i] :
( ( c_Binomial_Obinomial @ V_y @ ( c_Suc @ c_0 ) )
= V_y ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(31,plain,
( ( ! [V_U: $i,V_W: $i,V_V: $i] :
( ( V_U = V_W )
| ( V_V = V_W )
| ( V_U = V_V )
| ( c_in @ ( c_Message_Omsg_ONonce @ V_W ) @ ( c_Event_Oused @ v_evs_H_H ) @ tc_Message_Omsg )
| ( 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)],[16]) ).
thf(32,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[17]) ).
thf(33,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_minus @ V_m @ V_n @ tc_nat )
!= c_0 )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(34,plain,
( ( ! [V_U: $i,V_W: $i] :
( ( V_U = V_W )
| ! [V_V: $i] :
( ( V_V = V_W )
| ( V_U = V_V )
| ( c_in @ ( c_Message_Omsg_ONonce @ V_W ) @ ( c_Event_Oused @ v_evs_H_H ) @ tc_Message_Omsg )
| ( 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(extcnf_combined,[status(esa)],[31]) ).
thf(35,plain,
( ( ! [V_U: $i,V_W: $i] :
( ( V_U = V_W )
| ! [V_V: $i] :
( ( V_V = V_W )
| ( V_U = V_V )
| ( c_in @ ( c_Message_Omsg_ONonce @ V_W ) @ ( c_Event_Oused @ v_evs_H_H ) @ tc_Message_Omsg )
| ( 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)],[34]) ).
thf(36,plain,
( ( ! [V_y: $i] :
( ( c_Binomial_Obinomial @ V_y @ ( c_Suc @ c_0 ) )
= V_y ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(37,plain,
( ( ! [V_n: $i,V_k: $i] :
( ( c_Binomial_Obinomial @ ( c_Suc @ V_n ) @ ( c_Suc @ V_k ) )
= ( c_plus @ ( c_Binomial_Obinomial @ V_n @ V_k ) @ ( c_Binomial_Obinomial @ V_n @ ( c_Suc @ V_k ) ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(38,plain,
( ( ! [V_n: $i] :
( ( c_Binomial_Obinomial @ V_n @ c_0 )
= c_1 ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(39,plain,
( ( c_1
= ( c_Suc @ c_0 ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(40,plain,
( ( ! [V_m: $i,V_n: $i] :
( ( ( c_minus @ V_m @ V_n @ tc_nat )
!= c_0 )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(41,plain,
( ( ! [V_m: $i] :
( ( c_minus @ V_m @ V_m @ tc_nat )
= c_0 ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(42,plain,
( ( ! [V_n: $i,V_m: $i] : ( c_lessequals @ V_n @ ( c_plus @ V_n @ V_m @ tc_nat ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[24]) ).
thf(43,plain,
( ( ! [V_n: $i] : ( c_less @ V_n @ ( c_Suc @ V_n ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(44,plain,
( ( ! [V_m: $i,V_n: $i] :
( ~ ( c_lessequals @ V_m @ V_n @ tc_nat )
| ( c_less @ V_m @ ( c_Suc @ V_n ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[22]) ).
thf(45,plain,
( ( ! [V_k: $i,V_m: $i,V_n: $i] :
( ~ ( c_lessequals @ ( c_plus @ V_k @ V_m @ tc_nat ) @ ( c_plus @ V_k @ V_n @ tc_nat ) @ tc_nat )
| ( c_lessequals @ V_m @ V_n @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[21]) ).
thf(46,plain,
( ( ! [V_j: $i,V_i: $i] :
~ ( c_less @ ( c_plus @ V_j @ V_i @ tc_nat ) @ V_i @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[20]) ).
thf(47,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)],[19]) ).
thf(48,plain,
( ( ! [V_u: $i] :
( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatMost @ V_u @ tc_nat ) @ tc_nat )
= ( c_Suc @ V_u ) ) )
= $true ),
inference(copy,[status(thm)],[18]) ).
thf(49,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[32]) ).
thf(50,plain,
! [SV1: $i] :
( ( ! [SY23: $i] :
( ( SV1 = SY23 )
| ! [SY24: $i] :
( ( SY24 = SY23 )
| ( SV1 = SY24 )
| ( c_in @ ( c_Message_Omsg_ONonce @ SY23 ) @ ( c_Event_Oused @ v_evs_H_H ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ SY24 ) @ ( 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)],[35]) ).
thf(51,plain,
! [SV2: $i] :
( ( ( c_Binomial_Obinomial @ SV2 @ ( c_Suc @ c_0 ) )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[36]) ).
thf(52,plain,
! [SV3: $i] :
( ( ! [SY25: $i] :
( ( c_Binomial_Obinomial @ ( c_Suc @ SV3 ) @ ( c_Suc @ SY25 ) )
= ( c_plus @ ( c_Binomial_Obinomial @ SV3 @ SY25 ) @ ( c_Binomial_Obinomial @ SV3 @ ( c_Suc @ SY25 ) ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[37]) ).
thf(53,plain,
! [SV4: $i] :
( ( ( c_Binomial_Obinomial @ SV4 @ c_0 )
= c_1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[38]) ).
thf(54,plain,
! [SV5: $i] :
( ( ! [SY26: $i] :
( ( ( c_minus @ SV5 @ SY26 @ tc_nat )
!= c_0 )
| ( c_lessequals @ SV5 @ SY26 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[40]) ).
thf(55,plain,
! [SV6: $i] :
( ( ( c_minus @ SV6 @ SV6 @ tc_nat )
= c_0 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[41]) ).
thf(56,plain,
! [SV7: $i] :
( ( ! [SY27: $i] : ( c_lessequals @ SV7 @ ( c_plus @ SV7 @ SY27 @ tc_nat ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[42]) ).
thf(57,plain,
! [SV8: $i] :
( ( c_less @ SV8 @ ( c_Suc @ SV8 ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[43]) ).
thf(58,plain,
! [SV9: $i] :
( ( ! [SY28: $i] :
( ~ ( c_lessequals @ SV9 @ SY28 @ tc_nat )
| ( c_less @ SV9 @ ( c_Suc @ SY28 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[44]) ).
thf(59,plain,
! [SV10: $i] :
( ( ! [SY29: $i,SY30: $i] :
( ~ ( c_lessequals @ ( c_plus @ SV10 @ SY29 @ tc_nat ) @ ( c_plus @ SV10 @ SY30 @ tc_nat ) @ tc_nat )
| ( c_lessequals @ SY29 @ SY30 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[45]) ).
thf(60,plain,
! [SV11: $i] :
( ( ! [SY31: $i] :
~ ( c_less @ ( c_plus @ SV11 @ SY31 @ tc_nat ) @ SY31 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[46]) ).
thf(61,plain,
! [SV12: $i] :
( ( ! [SY32: $i] :
( ~ ( c_in @ ( c_Message_Omsg_ONonce @ SV12 ) @ ( c_Event_Oused @ SY32 ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ ( v_sko__urX @ SY32 ) @ SV12 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[47]) ).
thf(62,plain,
! [SV13: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_SetInterval_OatMost @ SV13 @ tc_nat ) @ tc_nat )
= ( c_Suc @ SV13 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(63,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[49]) ).
thf(64,plain,
! [SV14: $i,SV1: $i] :
( ( ( SV1 = SV14 )
| ! [SY33: $i] :
( ( SY33 = SV14 )
| ( SV1 = SY33 )
| ( c_in @ ( c_Message_Omsg_ONonce @ SV14 ) @ ( c_Event_Oused @ v_evs_H_H ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ SY33 ) @ ( 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)],[50]) ).
thf(65,plain,
! [SV15: $i,SV3: $i] :
( ( ( c_Binomial_Obinomial @ ( c_Suc @ SV3 ) @ ( c_Suc @ SV15 ) )
= ( c_plus @ ( c_Binomial_Obinomial @ SV3 @ SV15 ) @ ( c_Binomial_Obinomial @ SV3 @ ( c_Suc @ SV15 ) ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(66,plain,
! [SV16: $i,SV5: $i] :
( ( ( ( c_minus @ SV5 @ SV16 @ tc_nat )
!= c_0 )
| ( c_lessequals @ SV5 @ SV16 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(67,plain,
! [SV17: $i,SV7: $i] :
( ( c_lessequals @ SV7 @ ( c_plus @ SV7 @ SV17 @ tc_nat ) @ tc_nat )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(68,plain,
! [SV18: $i,SV9: $i] :
( ( ~ ( c_lessequals @ SV9 @ SV18 @ tc_nat )
| ( c_less @ SV9 @ ( c_Suc @ SV18 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(69,plain,
! [SV19: $i,SV10: $i] :
( ( ! [SY34: $i] :
( ~ ( c_lessequals @ ( c_plus @ SV10 @ SV19 @ tc_nat ) @ ( c_plus @ SV10 @ SY34 @ tc_nat ) @ tc_nat )
| ( c_lessequals @ SV19 @ SY34 @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(70,plain,
! [SV20: $i,SV11: $i] :
( ( ~ ( c_less @ ( c_plus @ SV11 @ SV20 @ tc_nat ) @ SV20 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(71,plain,
! [SV21: $i,SV12: $i] :
( ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ SV12 ) @ ( c_Event_Oused @ SV21 ) @ tc_Message_Omsg )
| ~ ( c_lessequals @ ( v_sko__urX @ SV21 ) @ SV12 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(72,plain,
! [SV14: $i,SV1: $i] :
( ( ( SV1 = SV14 )
= $true )
| ( ( ! [SY33: $i] :
( ( SY33 = SV14 )
| ( SV1 = SY33 )
| ( c_in @ ( c_Message_Omsg_ONonce @ SV14 ) @ ( c_Event_Oused @ v_evs_H_H ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ SY33 ) @ ( 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)],[64]) ).
thf(73,plain,
! [SV16: $i,SV5: $i] :
( ( ( ( c_minus @ SV5 @ SV16 @ tc_nat )
!= c_0 )
= $true )
| ( ( c_lessequals @ SV5 @ SV16 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[66]) ).
thf(74,plain,
! [SV18: $i,SV9: $i] :
( ( ( ~ ( c_lessequals @ SV9 @ SV18 @ tc_nat ) )
= $true )
| ( ( c_less @ SV9 @ ( c_Suc @ SV18 ) @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[68]) ).
thf(75,plain,
! [SV22: $i,SV19: $i,SV10: $i] :
( ( ~ ( c_lessequals @ ( c_plus @ SV10 @ SV19 @ tc_nat ) @ ( c_plus @ SV10 @ SV22 @ tc_nat ) @ tc_nat )
| ( c_lessequals @ SV19 @ SV22 @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(76,plain,
! [SV20: $i,SV11: $i] :
( ( c_less @ ( c_plus @ SV11 @ SV20 @ tc_nat ) @ SV20 @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(77,plain,
! [SV21: $i,SV12: $i] :
( ( ( ~ ( c_in @ ( c_Message_Omsg_ONonce @ SV12 ) @ ( c_Event_Oused @ SV21 ) @ tc_Message_Omsg ) )
= $true )
| ( ( ~ ( c_lessequals @ ( v_sko__urX @ SV21 ) @ SV12 @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[71]) ).
thf(78,plain,
! [SV1: $i,SV14: $i,SV23: $i] :
( ( ( ( SV23 = SV14 )
| ( SV1 = SV23 )
| ( c_in @ ( c_Message_Omsg_ONonce @ SV14 ) @ ( c_Event_Oused @ v_evs_H_H ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ SV23 ) @ ( 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 )
| ( ( SV1 = SV14 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(79,plain,
! [SV16: $i,SV5: $i] :
( ( ( ( c_minus @ SV5 @ SV16 @ tc_nat )
= c_0 )
= $false )
| ( ( c_lessequals @ SV5 @ SV16 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(80,plain,
! [SV18: $i,SV9: $i] :
( ( ( c_lessequals @ SV9 @ SV18 @ tc_nat )
= $false )
| ( ( c_less @ SV9 @ ( c_Suc @ SV18 ) @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[74]) ).
thf(81,plain,
! [SV22: $i,SV19: $i,SV10: $i] :
( ( ( ~ ( c_lessequals @ ( c_plus @ SV10 @ SV19 @ tc_nat ) @ ( c_plus @ SV10 @ SV22 @ tc_nat ) @ tc_nat ) )
= $true )
| ( ( c_lessequals @ SV19 @ SV22 @ tc_nat )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[75]) ).
thf(82,plain,
! [SV21: $i,SV12: $i] :
( ( ( c_in @ ( c_Message_Omsg_ONonce @ SV12 ) @ ( c_Event_Oused @ SV21 ) @ tc_Message_Omsg )
= $false )
| ( ( ~ ( c_lessequals @ ( v_sko__urX @ SV21 ) @ SV12 @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(83,plain,
! [SV1: $i,SV14: $i,SV23: $i] :
( ( ( SV23 = SV14 )
= $true )
| ( ( ( SV1 = SV23 )
| ( c_in @ ( c_Message_Omsg_ONonce @ SV14 ) @ ( c_Event_Oused @ v_evs_H_H ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ SV23 ) @ ( 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 )
| ( ( SV1 = SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[78]) ).
thf(84,plain,
! [SV22: $i,SV19: $i,SV10: $i] :
( ( ( c_lessequals @ ( c_plus @ SV10 @ SV19 @ tc_nat ) @ ( c_plus @ SV10 @ SV22 @ tc_nat ) @ tc_nat )
= $false )
| ( ( c_lessequals @ SV19 @ SV22 @ tc_nat )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[81]) ).
thf(85,plain,
! [SV12: $i,SV21: $i] :
( ( ( c_lessequals @ ( v_sko__urX @ SV21 ) @ SV12 @ tc_nat )
= $false )
| ( ( c_in @ ( c_Message_Omsg_ONonce @ SV12 ) @ ( c_Event_Oused @ SV21 ) @ tc_Message_Omsg )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[82]) ).
thf(86,plain,
! [SV14: $i,SV23: $i,SV1: $i] :
( ( ( SV1 = SV23 )
= $true )
| ( ( ( c_in @ ( c_Message_Omsg_ONonce @ SV14 ) @ ( c_Event_Oused @ v_evs_H_H ) @ tc_Message_Omsg )
| ( c_in @ ( c_Message_Omsg_ONonce @ SV23 ) @ ( 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 )
| ( ( SV23 = SV14 )
= $true )
| ( ( SV1 = SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[83]) ).
thf(87,plain,
! [SV1: $i,SV23: $i,SV14: $i] :
( ( ( c_in @ ( c_Message_Omsg_ONonce @ SV14 ) @ ( c_Event_Oused @ v_evs_H_H ) @ tc_Message_Omsg )
= $true )
| ( ( ( c_in @ ( c_Message_Omsg_ONonce @ SV23 ) @ ( 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 )
| ( ( SV1 = SV23 )
= $true )
| ( ( SV23 = SV14 )
= $true )
| ( ( SV1 = SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(88,plain,
! [SV14: $i,SV1: $i,SV23: $i] :
( ( ( c_in @ ( c_Message_Omsg_ONonce @ SV23 ) @ ( 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 )
| ( ( c_in @ ( c_Message_Omsg_ONonce @ SV14 ) @ ( c_Event_Oused @ v_evs_H_H ) @ tc_Message_Omsg )
= $true )
| ( ( SV1 = SV23 )
= $true )
| ( ( SV23 = SV14 )
= $true )
| ( ( SV1 = SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(89,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[39,88,85,84,80,79,76,67,65,63,62,57,55,53,51]) ).
thf(90,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV282-2 : 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
% 0.09/0.18 % Computer : n016.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 16:27:59 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 37.24/6.46
% 37.24/6.46 No.of.Axioms: 14
% 37.24/6.46
% 37.24/6.46 Length.of.Defs: 0
% 37.24/6.46
% 37.24/6.46 Contains.Choice.Funs: false
% 37.24/6.46 ..
% 37.24/6.46
% 37.24/6.46 ********************************
% 37.24/6.46 * All subproblems solved! *
% 37.24/6.46 ********************************
% 37.24/6.46 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:14,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:89,loop_count:0,foatp_calls:1,translation:fof_experiment)
% 37.24/6.46
% 37.24/6.46 %**** Beginning of derivation protocol ****
% 37.24/6.46 % SZS output start CNFRefutation
% See solution above
% 37.24/6.46
% 37.24/6.46 %**** End of derivation protocol ****
% 37.24/6.46 %**** no. of clauses in derivation: 90 ****
% 37.24/6.46 %**** clause counter: 89 ****
% 37.24/6.46
% 37.24/6.46 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:14,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:89,loop_count:0,foatp_calls:1,translation:fof_experiment)
%------------------------------------------------------------------------------