TSTP Solution File: SWV276-2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : SWV276-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 20:11:32 EDT 2022
% Result : Unsatisfiable 1.58s 1.80s
% Output : CNFRefutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 38
% Syntax : Number of formulae : 148 ( 94 unt; 18 typ; 0 def)
% Number of atoms : 533 ( 172 equ; 0 cnn)
% Maximal formula atoms : 3 ( 4 avg)
% Number of connectives : 1379 ( 83 ~; 121 |; 0 &;1175 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 8 con; 0-3 aty)
% Number of variables : 293 ( 0 ^ 293 !; 0 ?; 293 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_c_Message_Oanalz,type,
c_Message_Oanalz: $i > $i ).
thf(tp_c_Message_OinvKey,type,
c_Message_OinvKey: $i > $i ).
thf(tp_c_Message_OkeysFor,type,
c_Message_OkeysFor: $i > $i ).
thf(tp_c_Message_Omsg_OKey,type,
c_Message_Omsg_OKey: $i > $i ).
thf(tp_c_Message_Oparts,type,
c_Message_Oparts: $i > $i ).
thf(tp_c_Message_Osynth,type,
c_Message_Osynth: $i > $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_union,type,
c_union: $i > $i > $i > $i ).
thf(tp_tc_Message_Omsg,type,
tc_Message_Omsg: $i ).
thf(tp_tc_nat,type,
tc_nat: $i ).
thf(tp_tc_set,type,
tc_set: $i > $i ).
thf(tp_v_G,type,
v_G: $i ).
thf(tp_v_H,type,
v_H: $i ).
thf(tp_v_K,type,
v_K: $i ).
thf(tp_v_X,type,
v_X: $i ).
thf(tp_v_sko__uhi,type,
v_sko__uhi: $i > $i > $i ).
thf(1,axiom,
! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ~ ( c_in @ V_c @ V_B @ T_a )
| ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
thf(2,axiom,
! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
thf(3,axiom,
! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a )
| ( c_in @ V_c @ V_B @ T_a )
| ( c_in @ V_c @ V_A @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).
thf(4,axiom,
! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_in @ V_c @ V_B @ T_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(5,axiom,
! [V_G: $i,V_H: $i] :
( ( c_Message_Oparts @ ( c_union @ V_G @ V_H @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_Oparts @ V_G ) @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__Un_0) ).
thf(6,axiom,
! [V_H: $i] :
( ( c_Message_Oparts @ ( c_Message_Osynth @ V_H ) )
= ( c_union @ ( c_Message_Oparts @ V_H ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__synth_0) ).
thf(7,axiom,
! [V_X: $i,V_G: $i,V_H: $i] :
( ~ ( c_in @ V_X @ V_G @ tc_Message_Omsg )
| ( c_lessequals @ ( c_Message_Oparts @ ( c_insert @ V_X @ V_H @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Oparts @ V_G ) @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__insert__subset__Un_0) ).
thf(8,axiom,
! [V_H: $i] :
( ( c_Message_Oparts @ ( c_Message_Oanalz @ V_H ) )
= ( c_Message_Oparts @ V_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oparts__analz_0) ).
thf(9,axiom,
! [V_H: $i,V_H_H: $i] :
( ( c_Message_OkeysFor @ ( c_union @ V_H @ V_H_H @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_OkeysFor @ V_H ) @ ( c_Message_OkeysFor @ V_H_H ) @ tc_nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__Un_0) ).
thf(10,axiom,
! [V_G: $i,V_H: $i] :
( ~ ( c_lessequals @ V_G @ V_H @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_OkeysFor @ V_G ) @ ( c_Message_OkeysFor @ V_H ) @ ( tc_set @ tc_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OkeysFor__mono_0) ).
thf(11,axiom,
! [V_y: $i] :
( ( c_Message_OinvKey @ ( c_Message_OinvKey @ V_y ) )
= V_y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0) ).
thf(12,axiom,
! [V_H: $i] : ( c_lessequals @ ( c_Message_Oanalz @ V_H ) @ ( c_Message_Oparts @ V_H ) @ ( tc_set @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__parts_0) ).
thf(13,axiom,
! [V_X: $i,V_H: $i] :
( ~ ( c_in @ V_X @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
| ( c_in @ V_X @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Message_Oanalz__conj__parts_0) ).
thf(14,axiom,
! [V_K: $i,V_H: $i] :
( ~ ( c_in @ V_K @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ V_H ) ) @ tc_nat )
| ( c_in @ V_K @ ( c_Message_OkeysFor @ V_H ) @ tc_nat )
| ( V_K
= ( c_Message_OinvKey @ ( v_sko__uhi @ V_H @ V_K ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_1) ).
thf(15,axiom,
! [V_K: $i,V_H: $i] :
( ~ ( c_in @ V_K @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ V_H ) ) @ tc_nat )
| ( c_in @ V_K @ ( c_Message_OkeysFor @ V_H ) @ tc_nat )
| ( c_in @ ( c_Message_Omsg_OKey @ ( v_sko__uhi @ V_H @ V_K ) ) @ V_H @ tc_Message_Omsg ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_0) ).
thf(16,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(17,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[16]) ).
thf(18,negated_conjecture,
~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ v_K ) ) @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(19,negated_conjecture,
~ ( c_in @ v_K @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) ) @ tc_nat ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(20,negated_conjecture,
c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_H ) ) @ tc_Message_Omsg,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(21,negated_conjecture,
c_in @ v_K @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_insert @ v_X @ v_G @ tc_Message_Omsg ) ) ) @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(22,plain,
$false = $false,
inference(unfold_def,[status(thm)],[17]) ).
thf(23,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i,V_A: $i] :
( ~ ( c_in @ V_c @ V_B @ T_a )
| ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(24,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(25,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a )
| ( c_in @ V_c @ V_B @ T_a )
| ( c_in @ V_c @ V_A @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(26,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i,V_B: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_in @ V_c @ V_B @ T_a ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(27,plain,
( ( ! [V_G: $i,V_H: $i] :
( ( c_Message_Oparts @ ( c_union @ V_G @ V_H @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_Oparts @ V_G ) @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(28,plain,
( ( ! [V_H: $i] :
( ( c_Message_Oparts @ ( c_Message_Osynth @ V_H ) )
= ( c_union @ ( c_Message_Oparts @ V_H ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(29,plain,
( ( ! [V_X: $i,V_G: $i,V_H: $i] :
( ~ ( c_in @ V_X @ V_G @ tc_Message_Omsg )
| ( c_lessequals @ ( c_Message_Oparts @ ( c_insert @ V_X @ V_H @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Oparts @ V_G ) @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(30,plain,
( ( ! [V_H: $i] :
( ( c_Message_Oparts @ ( c_Message_Oanalz @ V_H ) )
= ( c_Message_Oparts @ V_H ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(31,plain,
( ( ! [V_H: $i,V_H_H: $i] :
( ( c_Message_OkeysFor @ ( c_union @ V_H @ V_H_H @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_OkeysFor @ V_H ) @ ( c_Message_OkeysFor @ V_H_H ) @ tc_nat ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(32,plain,
( ( ! [V_G: $i,V_H: $i] :
( ~ ( c_lessequals @ V_G @ V_H @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_OkeysFor @ V_G ) @ ( c_Message_OkeysFor @ V_H ) @ ( tc_set @ tc_nat ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(33,plain,
( ( ! [V_y: $i] :
( ( c_Message_OinvKey @ ( c_Message_OinvKey @ V_y ) )
= V_y ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(34,plain,
( ( ! [V_H: $i] : ( c_lessequals @ ( c_Message_Oanalz @ V_H ) @ ( c_Message_Oparts @ V_H ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(35,plain,
( ( ! [V_X: $i,V_H: $i] :
( ~ ( c_in @ V_X @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
| ( c_in @ V_X @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(36,plain,
( ( ! [V_K: $i,V_H: $i] :
( ~ ( c_in @ V_K @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ V_H ) ) @ tc_nat )
| ( c_in @ V_K @ ( c_Message_OkeysFor @ V_H ) @ tc_nat )
| ( V_K
= ( c_Message_OinvKey @ ( v_sko__uhi @ V_H @ V_K ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(37,plain,
( ( ! [V_K: $i,V_H: $i] :
( ~ ( c_in @ V_K @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ V_H ) ) @ tc_nat )
| ( c_in @ V_K @ ( c_Message_OkeysFor @ V_H ) @ tc_nat )
| ( c_in @ ( c_Message_Omsg_OKey @ ( v_sko__uhi @ V_H @ V_K ) ) @ V_H @ tc_Message_Omsg ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(38,plain,
( ( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ v_K ) ) @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(39,plain,
( ( ~ ( c_in @ v_K @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) ) @ tc_nat ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(40,plain,
( ( c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_H ) ) @ tc_Message_Omsg )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(41,plain,
( ( c_in @ v_K @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_insert @ v_X @ v_G @ tc_Message_Omsg ) ) ) @ tc_nat )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(42,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(43,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_c @ V_B @ T_a )
| ! [V_A: $i] : ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[23]) ).
thf(44,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ! [V_B: $i] : ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(45,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ! [V_B: $i] :
( ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_in @ V_c @ V_B @ T_a ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(46,plain,
( ( ! [V_X: $i,V_G: $i] :
( ~ ( c_in @ V_X @ V_G @ tc_Message_Omsg )
| ! [V_H: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_insert @ V_X @ V_H @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Oparts @ V_G ) @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(47,plain,
( ( ! [V_K: $i,V_H: $i] :
( ~ ( c_in @ V_K @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ V_H ) ) @ tc_nat )
| ( V_K
= ( c_Message_OinvKey @ ( v_sko__uhi @ V_H @ V_K ) ) )
| ( c_in @ V_K @ ( c_Message_OkeysFor @ V_H ) @ tc_nat ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(48,plain,
( ( c_in @ v_K @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_insert @ v_X @ v_G @ tc_Message_Omsg ) ) ) @ tc_nat )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(49,plain,
( ( c_in @ v_X @ ( c_Message_Osynth @ ( c_Message_Oanalz @ v_H ) ) @ tc_Message_Omsg )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(50,plain,
( ( ~ ( c_in @ v_K @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) ) @ tc_nat ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(51,plain,
( ( ~ ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ v_K ) ) @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(52,plain,
( ( ! [V_K: $i,V_H: $i] :
( ~ ( c_in @ V_K @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ V_H ) ) @ tc_nat )
| ( c_in @ V_K @ ( c_Message_OkeysFor @ V_H ) @ tc_nat )
| ( c_in @ ( c_Message_Omsg_OKey @ ( v_sko__uhi @ V_H @ V_K ) ) @ V_H @ tc_Message_Omsg ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(53,plain,
( ( ! [V_K: $i,V_H: $i] :
( ~ ( c_in @ V_K @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ V_H ) ) @ tc_nat )
| ( V_K
= ( c_Message_OinvKey @ ( v_sko__uhi @ V_H @ V_K ) ) )
| ( c_in @ V_K @ ( c_Message_OkeysFor @ V_H ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(54,plain,
( ( ! [V_X: $i,V_H: $i] :
( ~ ( c_in @ V_X @ ( c_Message_Oanalz @ V_H ) @ tc_Message_Omsg )
| ( c_in @ V_X @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(55,plain,
( ( ! [V_H: $i] : ( c_lessequals @ ( c_Message_Oanalz @ V_H ) @ ( c_Message_Oparts @ V_H ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(56,plain,
( ( ! [V_y: $i] :
( ( c_Message_OinvKey @ ( c_Message_OinvKey @ V_y ) )
= V_y ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(57,plain,
( ( ! [V_G: $i,V_H: $i] :
( ~ ( c_lessequals @ V_G @ V_H @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_OkeysFor @ V_G ) @ ( c_Message_OkeysFor @ V_H ) @ ( tc_set @ tc_nat ) ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(58,plain,
( ( ! [V_H: $i,V_H_H: $i] :
( ( c_Message_OkeysFor @ ( c_union @ V_H @ V_H_H @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_OkeysFor @ V_H ) @ ( c_Message_OkeysFor @ V_H_H ) @ tc_nat ) ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(59,plain,
( ( ! [V_H: $i] :
( ( c_Message_Oparts @ ( c_Message_Oanalz @ V_H ) )
= ( c_Message_Oparts @ V_H ) ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(60,plain,
( ( ! [V_X: $i,V_G: $i] :
( ~ ( c_in @ V_X @ V_G @ tc_Message_Omsg )
| ! [V_H: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_insert @ V_X @ V_H @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Oparts @ V_G ) @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(61,plain,
( ( ! [V_H: $i] :
( ( c_Message_Oparts @ ( c_Message_Osynth @ V_H ) )
= ( c_union @ ( c_Message_Oparts @ V_H ) @ ( c_Message_Osynth @ V_H ) @ tc_Message_Omsg ) ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(62,plain,
( ( ! [V_G: $i,V_H: $i] :
( ( c_Message_Oparts @ ( c_union @ V_G @ V_H @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_Oparts @ V_G ) @ ( c_Message_Oparts @ V_H ) @ tc_Message_Omsg ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(63,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ! [V_B: $i] :
( ~ ( c_lessequals @ V_A @ V_B @ ( tc_set @ T_a ) )
| ( c_in @ V_c @ V_B @ T_a ) ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(64,plain,
( ( ! [V_c: $i,V_A: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a )
| ( c_in @ V_c @ V_B @ T_a )
| ( c_in @ V_c @ V_A @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(65,plain,
( ( ! [V_c: $i,V_A: $i,T_a: $i] :
( ~ ( c_in @ V_c @ V_A @ T_a )
| ! [V_B: $i] : ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(66,plain,
( ( ! [V_c: $i,V_B: $i,T_a: $i] :
( ~ ( c_in @ V_c @ V_B @ T_a )
| ! [V_A: $i] : ( c_in @ V_c @ ( c_union @ V_A @ V_B @ T_a ) @ T_a ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(67,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(68,plain,
( ( c_in @ v_K @ ( c_Message_OkeysFor @ ( c_Message_Oparts @ ( c_union @ v_G @ v_H @ tc_Message_Omsg ) ) ) @ tc_nat )
= $false ),
inference(extcnf_not_pos,[status(thm)],[50]) ).
thf(69,plain,
( ( c_in @ ( c_Message_Omsg_OKey @ ( c_Message_OinvKey @ v_K ) ) @ ( c_Message_Oparts @ v_H ) @ tc_Message_Omsg )
= $false ),
inference(extcnf_not_pos,[status(thm)],[51]) ).
thf(70,plain,
! [SV1: $i] :
( ( ! [SY35: $i] :
( ~ ( c_in @ SV1 @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ SY35 ) ) @ tc_nat )
| ( c_in @ SV1 @ ( c_Message_OkeysFor @ SY35 ) @ tc_nat )
| ( c_in @ ( c_Message_Omsg_OKey @ ( v_sko__uhi @ SY35 @ SV1 ) ) @ SY35 @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(71,plain,
! [SV2: $i] :
( ( ! [SY36: $i] :
( ~ ( c_in @ SV2 @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ SY36 ) ) @ tc_nat )
| ( SV2
= ( c_Message_OinvKey @ ( v_sko__uhi @ SY36 @ SV2 ) ) )
| ( c_in @ SV2 @ ( c_Message_OkeysFor @ SY36 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(72,plain,
! [SV3: $i] :
( ( ! [SY37: $i] :
( ~ ( c_in @ SV3 @ ( c_Message_Oanalz @ SY37 ) @ tc_Message_Omsg )
| ( c_in @ SV3 @ ( c_Message_Oparts @ SY37 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(73,plain,
! [SV4: $i] :
( ( c_lessequals @ ( c_Message_Oanalz @ SV4 ) @ ( c_Message_Oparts @ SV4 ) @ ( tc_set @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(74,plain,
! [SV5: $i] :
( ( ( c_Message_OinvKey @ ( c_Message_OinvKey @ SV5 ) )
= SV5 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(75,plain,
! [SV6: $i] :
( ( ! [SY38: $i] :
( ~ ( c_lessequals @ SV6 @ SY38 @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_OkeysFor @ SV6 ) @ ( c_Message_OkeysFor @ SY38 ) @ ( tc_set @ tc_nat ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(76,plain,
! [SV7: $i] :
( ( ! [SY39: $i] :
( ( c_Message_OkeysFor @ ( c_union @ SV7 @ SY39 @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_OkeysFor @ SV7 ) @ ( c_Message_OkeysFor @ SY39 ) @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(77,plain,
! [SV8: $i] :
( ( ( c_Message_Oparts @ ( c_Message_Oanalz @ SV8 ) )
= ( c_Message_Oparts @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(78,plain,
! [SV9: $i] :
( ( ! [SY40: $i] :
( ~ ( c_in @ SV9 @ SY40 @ tc_Message_Omsg )
| ! [SY41: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_insert @ SV9 @ SY41 @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Oparts @ SY40 ) @ ( c_Message_Oparts @ SY41 ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(79,plain,
! [SV10: $i] :
( ( ( c_Message_Oparts @ ( c_Message_Osynth @ SV10 ) )
= ( c_union @ ( c_Message_Oparts @ SV10 ) @ ( c_Message_Osynth @ SV10 ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(80,plain,
! [SV11: $i] :
( ( ! [SY42: $i] :
( ( c_Message_Oparts @ ( c_union @ SV11 @ SY42 @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_Oparts @ SV11 ) @ ( c_Message_Oparts @ SY42 ) @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(81,plain,
! [SV12: $i] :
( ( ! [SY43: $i,SY44: $i] :
( ~ ( c_in @ SV12 @ SY43 @ SY44 )
| ! [SY45: $i] :
( ~ ( c_lessequals @ SY43 @ SY45 @ ( tc_set @ SY44 ) )
| ( c_in @ SV12 @ SY45 @ SY44 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(82,plain,
! [SV13: $i] :
( ( ! [SY46: $i,SY47: $i,SY48: $i] :
( ~ ( c_in @ SV13 @ ( c_union @ SY46 @ SY47 @ SY48 ) @ SY48 )
| ( c_in @ SV13 @ SY47 @ SY48 )
| ( c_in @ SV13 @ SY46 @ SY48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(83,plain,
! [SV14: $i] :
( ( ! [SY49: $i,SY50: $i] :
( ~ ( c_in @ SV14 @ SY49 @ SY50 )
| ! [SY51: $i] : ( c_in @ SV14 @ ( c_union @ SY49 @ SY51 @ SY50 ) @ SY50 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(84,plain,
! [SV15: $i] :
( ( ! [SY52: $i,SY53: $i] :
( ~ ( c_in @ SV15 @ SY52 @ SY53 )
| ! [SY54: $i] : ( c_in @ SV15 @ ( c_union @ SY54 @ SY52 @ SY53 ) @ SY53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(85,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[67]) ).
thf(86,plain,
! [SV16: $i,SV1: $i] :
( ( ~ ( c_in @ SV1 @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ SV16 ) ) @ tc_nat )
| ( c_in @ SV1 @ ( c_Message_OkeysFor @ SV16 ) @ tc_nat )
| ( c_in @ ( c_Message_Omsg_OKey @ ( v_sko__uhi @ SV16 @ SV1 ) ) @ SV16 @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(87,plain,
! [SV17: $i,SV2: $i] :
( ( ~ ( c_in @ SV2 @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ SV17 ) ) @ tc_nat )
| ( SV2
= ( c_Message_OinvKey @ ( v_sko__uhi @ SV17 @ SV2 ) ) )
| ( c_in @ SV2 @ ( c_Message_OkeysFor @ SV17 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(88,plain,
! [SV18: $i,SV3: $i] :
( ( ~ ( c_in @ SV3 @ ( c_Message_Oanalz @ SV18 ) @ tc_Message_Omsg )
| ( c_in @ SV3 @ ( c_Message_Oparts @ SV18 ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(89,plain,
! [SV19: $i,SV6: $i] :
( ( ~ ( c_lessequals @ SV6 @ SV19 @ ( tc_set @ tc_Message_Omsg ) )
| ( c_lessequals @ ( c_Message_OkeysFor @ SV6 ) @ ( c_Message_OkeysFor @ SV19 ) @ ( tc_set @ tc_nat ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(90,plain,
! [SV20: $i,SV7: $i] :
( ( ( c_Message_OkeysFor @ ( c_union @ SV7 @ SV20 @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_OkeysFor @ SV7 ) @ ( c_Message_OkeysFor @ SV20 ) @ tc_nat ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(91,plain,
! [SV21: $i,SV9: $i] :
( ( ~ ( c_in @ SV9 @ SV21 @ tc_Message_Omsg )
| ! [SY55: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_insert @ SV9 @ SY55 @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Oparts @ SV21 ) @ ( c_Message_Oparts @ SY55 ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(92,plain,
! [SV22: $i,SV11: $i] :
( ( ( c_Message_Oparts @ ( c_union @ SV11 @ SV22 @ tc_Message_Omsg ) )
= ( c_union @ ( c_Message_Oparts @ SV11 ) @ ( c_Message_Oparts @ SV22 ) @ tc_Message_Omsg ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(93,plain,
! [SV23: $i,SV12: $i] :
( ( ! [SY56: $i] :
( ~ ( c_in @ SV12 @ SV23 @ SY56 )
| ! [SY57: $i] :
( ~ ( c_lessequals @ SV23 @ SY57 @ ( tc_set @ SY56 ) )
| ( c_in @ SV12 @ SY57 @ SY56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(94,plain,
! [SV24: $i,SV13: $i] :
( ( ! [SY58: $i,SY59: $i] :
( ~ ( c_in @ SV13 @ ( c_union @ SV24 @ SY58 @ SY59 ) @ SY59 )
| ( c_in @ SV13 @ SY58 @ SY59 )
| ( c_in @ SV13 @ SV24 @ SY59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(95,plain,
! [SV25: $i,SV14: $i] :
( ( ! [SY60: $i] :
( ~ ( c_in @ SV14 @ SV25 @ SY60 )
| ! [SY61: $i] : ( c_in @ SV14 @ ( c_union @ SV25 @ SY61 @ SY60 ) @ SY60 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(96,plain,
! [SV26: $i,SV15: $i] :
( ( ! [SY62: $i] :
( ~ ( c_in @ SV15 @ SV26 @ SY62 )
| ! [SY63: $i] : ( c_in @ SV15 @ ( c_union @ SY63 @ SV26 @ SY62 ) @ SY62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(97,plain,
! [SV16: $i,SV1: $i] :
( ( ( ~ ( c_in @ SV1 @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ SV16 ) ) @ tc_nat ) )
= $true )
| ( ( ( c_in @ SV1 @ ( c_Message_OkeysFor @ SV16 ) @ tc_nat )
| ( c_in @ ( c_Message_Omsg_OKey @ ( v_sko__uhi @ SV16 @ SV1 ) ) @ SV16 @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[86]) ).
thf(98,plain,
! [SV17: $i,SV2: $i] :
( ( ( ~ ( c_in @ SV2 @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ SV17 ) ) @ tc_nat ) )
= $true )
| ( ( ( SV2
= ( c_Message_OinvKey @ ( v_sko__uhi @ SV17 @ SV2 ) ) )
| ( c_in @ SV2 @ ( c_Message_OkeysFor @ SV17 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[87]) ).
thf(99,plain,
! [SV18: $i,SV3: $i] :
( ( ( ~ ( c_in @ SV3 @ ( c_Message_Oanalz @ SV18 ) @ tc_Message_Omsg ) )
= $true )
| ( ( c_in @ SV3 @ ( c_Message_Oparts @ SV18 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[88]) ).
thf(100,plain,
! [SV19: $i,SV6: $i] :
( ( ( ~ ( c_lessequals @ SV6 @ SV19 @ ( tc_set @ tc_Message_Omsg ) ) )
= $true )
| ( ( c_lessequals @ ( c_Message_OkeysFor @ SV6 ) @ ( c_Message_OkeysFor @ SV19 ) @ ( tc_set @ tc_nat ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[89]) ).
thf(101,plain,
! [SV21: $i,SV9: $i] :
( ( ( ~ ( c_in @ SV9 @ SV21 @ tc_Message_Omsg ) )
= $true )
| ( ( ! [SY55: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_insert @ SV9 @ SY55 @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Oparts @ SV21 ) @ ( c_Message_Oparts @ SY55 ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(102,plain,
! [SV27: $i,SV23: $i,SV12: $i] :
( ( ~ ( c_in @ SV12 @ SV23 @ SV27 )
| ! [SY64: $i] :
( ~ ( c_lessequals @ SV23 @ SY64 @ ( tc_set @ SV27 ) )
| ( c_in @ SV12 @ SY64 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(103,plain,
! [SV28: $i,SV24: $i,SV13: $i] :
( ( ! [SY65: $i] :
( ~ ( c_in @ SV13 @ ( c_union @ SV24 @ SV28 @ SY65 ) @ SY65 )
| ( c_in @ SV13 @ SV28 @ SY65 )
| ( c_in @ SV13 @ SV24 @ SY65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(104,plain,
! [SV29: $i,SV25: $i,SV14: $i] :
( ( ~ ( c_in @ SV14 @ SV25 @ SV29 )
| ! [SY66: $i] : ( c_in @ SV14 @ ( c_union @ SV25 @ SY66 @ SV29 ) @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(105,plain,
! [SV30: $i,SV26: $i,SV15: $i] :
( ( ~ ( c_in @ SV15 @ SV26 @ SV30 )
| ! [SY67: $i] : ( c_in @ SV15 @ ( c_union @ SY67 @ SV26 @ SV30 ) @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(106,plain,
! [SV16: $i,SV1: $i] :
( ( ( c_in @ SV1 @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ SV16 ) ) @ tc_nat )
= $false )
| ( ( ( c_in @ SV1 @ ( c_Message_OkeysFor @ SV16 ) @ tc_nat )
| ( c_in @ ( c_Message_Omsg_OKey @ ( v_sko__uhi @ SV16 @ SV1 ) ) @ SV16 @ tc_Message_Omsg ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[97]) ).
thf(107,plain,
! [SV17: $i,SV2: $i] :
( ( ( c_in @ SV2 @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ SV17 ) ) @ tc_nat )
= $false )
| ( ( ( SV2
= ( c_Message_OinvKey @ ( v_sko__uhi @ SV17 @ SV2 ) ) )
| ( c_in @ SV2 @ ( c_Message_OkeysFor @ SV17 ) @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[98]) ).
thf(108,plain,
! [SV18: $i,SV3: $i] :
( ( ( c_in @ SV3 @ ( c_Message_Oanalz @ SV18 ) @ tc_Message_Omsg )
= $false )
| ( ( c_in @ SV3 @ ( c_Message_Oparts @ SV18 ) @ tc_Message_Omsg )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[99]) ).
thf(109,plain,
! [SV19: $i,SV6: $i] :
( ( ( c_lessequals @ SV6 @ SV19 @ ( tc_set @ tc_Message_Omsg ) )
= $false )
| ( ( c_lessequals @ ( c_Message_OkeysFor @ SV6 ) @ ( c_Message_OkeysFor @ SV19 ) @ ( tc_set @ tc_nat ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[100]) ).
thf(110,plain,
! [SV21: $i,SV9: $i] :
( ( ( c_in @ SV9 @ SV21 @ tc_Message_Omsg )
= $false )
| ( ( ! [SY55: $i] : ( c_lessequals @ ( c_Message_Oparts @ ( c_insert @ SV9 @ SY55 @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Oparts @ SV21 ) @ ( c_Message_Oparts @ SY55 ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(111,plain,
! [SV27: $i,SV23: $i,SV12: $i] :
( ( ( ~ ( c_in @ SV12 @ SV23 @ SV27 ) )
= $true )
| ( ( ! [SY64: $i] :
( ~ ( c_lessequals @ SV23 @ SY64 @ ( tc_set @ SV27 ) )
| ( c_in @ SV12 @ SY64 @ SV27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[102]) ).
thf(112,plain,
! [SV31: $i,SV28: $i,SV24: $i,SV13: $i] :
( ( ~ ( c_in @ SV13 @ ( c_union @ SV24 @ SV28 @ SV31 ) @ SV31 )
| ( c_in @ SV13 @ SV28 @ SV31 )
| ( c_in @ SV13 @ SV24 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(113,plain,
! [SV29: $i,SV25: $i,SV14: $i] :
( ( ( ~ ( c_in @ SV14 @ SV25 @ SV29 ) )
= $true )
| ( ( ! [SY66: $i] : ( c_in @ SV14 @ ( c_union @ SV25 @ SY66 @ SV29 ) @ SV29 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(114,plain,
! [SV30: $i,SV26: $i,SV15: $i] :
( ( ( ~ ( c_in @ SV15 @ SV26 @ SV30 ) )
= $true )
| ( ( ! [SY67: $i] : ( c_in @ SV15 @ ( c_union @ SY67 @ SV26 @ SV30 ) @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[105]) ).
thf(115,plain,
! [SV16: $i,SV1: $i] :
( ( ( c_in @ SV1 @ ( c_Message_OkeysFor @ SV16 ) @ tc_nat )
= $true )
| ( ( c_in @ ( c_Message_Omsg_OKey @ ( v_sko__uhi @ SV16 @ SV1 ) ) @ SV16 @ tc_Message_Omsg )
= $true )
| ( ( c_in @ SV1 @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ SV16 ) ) @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[106]) ).
thf(116,plain,
! [SV17: $i,SV2: $i] :
( ( ( SV2
= ( c_Message_OinvKey @ ( v_sko__uhi @ SV17 @ SV2 ) ) )
= $true )
| ( ( c_in @ SV2 @ ( c_Message_OkeysFor @ SV17 ) @ tc_nat )
= $true )
| ( ( c_in @ SV2 @ ( c_Message_OkeysFor @ ( c_Message_Osynth @ SV17 ) ) @ tc_nat )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[107]) ).
thf(117,plain,
! [SV21: $i,SV32: $i,SV9: $i] :
( ( ( c_lessequals @ ( c_Message_Oparts @ ( c_insert @ SV9 @ SV32 @ tc_Message_Omsg ) ) @ ( c_union @ ( c_Message_Oparts @ SV21 ) @ ( c_Message_Oparts @ SV32 ) @ tc_Message_Omsg ) @ ( tc_set @ tc_Message_Omsg ) )
= $true )
| ( ( c_in @ SV9 @ SV21 @ tc_Message_Omsg )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(118,plain,
! [SV27: $i,SV23: $i,SV12: $i] :
( ( ( c_in @ SV12 @ SV23 @ SV27 )
= $false )
| ( ( ! [SY64: $i] :
( ~ ( c_lessequals @ SV23 @ SY64 @ ( tc_set @ SV27 ) )
| ( c_in @ SV12 @ SY64 @ SV27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[111]) ).
thf(119,plain,
! [SV31: $i,SV28: $i,SV24: $i,SV13: $i] :
( ( ( ~ ( c_in @ SV13 @ ( c_union @ SV24 @ SV28 @ SV31 ) @ SV31 ) )
= $true )
| ( ( ( c_in @ SV13 @ SV28 @ SV31 )
| ( c_in @ SV13 @ SV24 @ SV31 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[112]) ).
thf(120,plain,
! [SV29: $i,SV25: $i,SV14: $i] :
( ( ( c_in @ SV14 @ SV25 @ SV29 )
= $false )
| ( ( ! [SY66: $i] : ( c_in @ SV14 @ ( c_union @ SV25 @ SY66 @ SV29 ) @ SV29 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[113]) ).
thf(121,plain,
! [SV30: $i,SV26: $i,SV15: $i] :
( ( ( c_in @ SV15 @ SV26 @ SV30 )
= $false )
| ( ( ! [SY67: $i] : ( c_in @ SV15 @ ( c_union @ SY67 @ SV26 @ SV30 ) @ SV30 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[114]) ).
thf(122,plain,
! [SV12: $i,SV27: $i,SV33: $i,SV23: $i] :
( ( ( ~ ( c_lessequals @ SV23 @ SV33 @ ( tc_set @ SV27 ) )
| ( c_in @ SV12 @ SV33 @ SV27 ) )
= $true )
| ( ( c_in @ SV12 @ SV23 @ SV27 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(123,plain,
! [SV31: $i,SV28: $i,SV24: $i,SV13: $i] :
( ( ( c_in @ SV13 @ ( c_union @ SV24 @ SV28 @ SV31 ) @ SV31 )
= $false )
| ( ( ( c_in @ SV13 @ SV28 @ SV31 )
| ( c_in @ SV13 @ SV24 @ SV31 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[119]) ).
thf(124,plain,
! [SV29: $i,SV34: $i,SV25: $i,SV14: $i] :
( ( ( c_in @ SV14 @ ( c_union @ SV25 @ SV34 @ SV29 ) @ SV29 )
= $true )
| ( ( c_in @ SV14 @ SV25 @ SV29 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(125,plain,
! [SV30: $i,SV26: $i,SV35: $i,SV15: $i] :
( ( ( c_in @ SV15 @ ( c_union @ SV35 @ SV26 @ SV30 ) @ SV30 )
= $true )
| ( ( c_in @ SV15 @ SV26 @ SV30 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(126,plain,
! [SV12: $i,SV27: $i,SV33: $i,SV23: $i] :
( ( ( ~ ( c_lessequals @ SV23 @ SV33 @ ( tc_set @ SV27 ) ) )
= $true )
| ( ( c_in @ SV12 @ SV33 @ SV27 )
= $true )
| ( ( c_in @ SV12 @ SV23 @ SV27 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[122]) ).
thf(127,plain,
! [SV24: $i,SV31: $i,SV28: $i,SV13: $i] :
( ( ( c_in @ SV13 @ SV28 @ SV31 )
= $true )
| ( ( c_in @ SV13 @ SV24 @ SV31 )
= $true )
| ( ( c_in @ SV13 @ ( c_union @ SV24 @ SV28 @ SV31 ) @ SV31 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[123]) ).
thf(128,plain,
! [SV12: $i,SV27: $i,SV33: $i,SV23: $i] :
( ( ( c_lessequals @ SV23 @ SV33 @ ( tc_set @ SV27 ) )
= $false )
| ( ( c_in @ SV12 @ SV33 @ SV27 )
= $true )
| ( ( c_in @ SV12 @ SV23 @ SV27 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[126]) ).
thf(129,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[48,128,127,125,124,117,116,115,109,108,92,90,85,79,77,74,73,69,68,49]) ).
thf(130,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[129]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV276-2 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.12 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Thu Jun 16 01:12:54 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35
% 0.13/0.35 No.of.Axioms: 19
% 0.13/0.35
% 0.13/0.35 Length.of.Defs: 0
% 0.13/0.35
% 0.13/0.35 Contains.Choice.Funs: false
% 0.13/0.36 (rf:0,axioms:19,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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:21,loop_count:0,foatp_calls:0,translation:fof_full).......
% 1.58/1.80
% 1.58/1.80 ********************************
% 1.58/1.80 * All subproblems solved! *
% 1.58/1.80 ********************************
% 1.58/1.80 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:19,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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:129,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.58/1.82
% 1.58/1.82 %**** Beginning of derivation protocol ****
% 1.58/1.82 % SZS output start CNFRefutation
% See solution above
% 1.58/1.82
% 1.58/1.82 %**** End of derivation protocol ****
% 1.58/1.82 %**** no. of clauses in derivation: 130 ****
% 1.58/1.82 %**** clause counter: 129 ****
% 1.58/1.82
% 1.58/1.82 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:19,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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:129,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------