%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV276-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n015.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 : Sun Sep 27 08:58:41 AM UTC 2026
% Result : Unsatisfiable 12.56s 4.37s
% Output : Refutation 11.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 19
% Syntax : Number of formulae : 123 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 274 ( 106 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 1450 ( 142 ~; 99 |; 0 &;1209 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 8 con; 0-3 aty)
% Number of variables : 168 ( 0 ^; 168 !; 0 ?; 168 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(v_K_decl,type,
v_K: $i ).
thf(c_Message_OkeysFor_decl,type,
c_Message_OkeysFor: $i > $i ).
thf(c_Message_Oparts_decl,type,
c_Message_Oparts: $i > $i ).
thf(c_insert_decl,type,
c_insert: $i > $i > $i > $i ).
thf(v_X_decl,type,
v_X: $i ).
thf(v_G_decl,type,
v_G: $i ).
thf(tc_Message_Omsg_decl,type,
tc_Message_Omsg: $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_Message_Osynth_decl,type,
c_Message_Osynth: $i > $i ).
thf(c_Message_Oanalz_decl,type,
c_Message_Oanalz: $i > $i ).
thf(v_H_decl,type,
v_H: $i ).
thf(c_union_decl,type,
c_union: $i > $i > $i > $i ).
thf(c_Message_Omsg_OKey_decl,type,
c_Message_Omsg_OKey: $i > $i ).
thf(c_Message_OinvKey_decl,type,
c_Message_OinvKey: $i > $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(tc_set_decl,type,
tc_set: $i > $i ).
thf(v_sko__uhi_decl,type,
v_sko__uhi: $i > $i > $i ).
thf(1,negated_conjecture,
tc_nat @ ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(20,plain,
tc_nat @ ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_1) ).
thf(33,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(34,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[33]) ).
thf(263,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( C @ ( B @ ( A @ c_in ) ) ) )
| ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,34]) ).
thf(264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_nat @ ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( C @ ( B @ ( A @ c_in ) ) ) )
| ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[263]) ).
thf(265,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ c_union ) ) @ ( v_K @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[264:[bind(A,$thf( v_K )),bind(B,$thf( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) @ c_Message_Oparts @ c_Message_OkeysFor )),bind(C,$thf( tc_nat )),bind(D,$thf( D ))]]) ).
thf(288,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ c_union ) ) @ ( v_K @ c_in ) ) ),
inference(simp,[status(thm)],[265]) ).
thf(3,negated_conjecture,
~ ( tc_nat @ ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(22,plain,
~ ( tc_nat @ ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(24,plain,
~ ( tc_nat @ ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[22]) ).
thf(327,plain,
! [A: $i] :
( ( ( tc_nat @ ( tc_nat @ ( A @ ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ c_union ) ) @ ( v_K @ c_in ) ) )
!= ( tc_nat @ ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[288,24]) ).
thf(328,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ ( A @ ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ c_union ) ) @ ( v_K @ c_in ) ) )
!= ( tc_nat @ ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[327]) ).
thf(340,plain,
! [A: $i] :
( ( tc_nat != tc_nat )
| ( ( tc_nat @ ( A @ ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ c_union ) ) )
!= ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( v_K != v_K ) ),
inference(simp,[status(thm)],[328]) ).
thf(347,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ c_union ) ) )
!= ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oparts @ c_Message_OkeysFor ) ),
inference(simp,[status(thm)],[340]) ).
thf(19,axiom,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__subset__parts_0) ).
thf(55,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( B @ c_Message_OkeysFor @ ( A @ c_Message_OkeysFor @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__mono_0) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( B @ c_Message_OkeysFor @ ( A @ c_Message_OkeysFor @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( tc_nat @ tc_set @ ( B @ c_Message_OkeysFor @ ( A @ c_Message_OkeysFor @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ tc_set @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(cnf,[status(esa)],[26]) ).
thf(121,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) )
| ( tc_nat @ tc_set @ ( C @ c_Message_OkeysFor @ ( B @ c_Message_OkeysFor @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[55,27]) ).
thf(122,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) )
| ( tc_nat @ tc_set @ ( C @ c_Message_OkeysFor @ ( B @ c_Message_OkeysFor @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[121]) ).
thf(123,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( A @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_Message_Oanalz @ c_Message_OkeysFor @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[122:[bind(A,$thf( E )),bind(B,$thf( E @ c_Message_Oanalz )),bind(C,$thf( E @ c_Message_Oparts ))]]) ).
thf(125,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( A @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_Message_Oanalz @ c_Message_OkeysFor @ c_lessequals ) ) ),
inference(simp,[status(thm)],[123]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_OkeysFor )
= ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_Message_OkeysFor @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OkeysFor__Un_0) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_OkeysFor )
= ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_Message_OkeysFor @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ c_Message_Osynth @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oparts @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__synth_0) ).
thf(41,plain,
! [A: $i] :
( ( A @ c_Message_Osynth @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( A @ c_Message_Osynth @ ( A @ c_Message_Oparts @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(69,plain,
( ( ( tc_nat @ ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( tc_nat @ ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,24]) ).
thf(70,plain,
( ( tc_nat @ ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( tc_nat @ ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(72,plain,
( ( tc_nat != tc_nat )
| ( ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oparts @ c_Message_OkeysFor )
!= ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( v_K != v_K ) ),
inference(simp,[status(thm)],[70]) ).
thf(73,plain,
( ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oparts @ c_Message_OkeysFor )
!= ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) @ c_Message_Oparts @ c_Message_OkeysFor ) ),
inference(simp,[status(thm)],[72]) ).
thf(14,axiom,
! [A: $i] :
( ( A @ c_Message_OinvKey @ c_Message_OinvKey )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0) ).
thf(45,plain,
! [A: $i] :
( ( A @ c_Message_OinvKey @ c_Message_OinvKey )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(46,plain,
! [A: $i] :
( ( A @ c_Message_OinvKey @ c_Message_OinvKey )
= A ),
inference(lifteq,[status(thm)],[45]) ).
thf(4,negated_conjecture,
~ ( tc_Message_Omsg @ ( v_H @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(23,plain,
~ ( tc_Message_Omsg @ ( v_H @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(25,plain,
~ ( tc_Message_Omsg @ ( v_H @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ),
inference(polarity_switch,[status(thm)],[23]) ).
thf(60,plain,
! [A: $i] :
( ( ( A @ c_Message_OinvKey @ c_Message_OinvKey )
!= ( v_K @ c_Message_OinvKey ) )
| ~ ( tc_Message_Omsg @ ( v_H @ c_Message_Oparts @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[46,25]) ).
thf(63,plain,
! [A: $i] :
( ( ( A @ c_Message_OinvKey )
!= v_K )
| ~ ( tc_Message_Omsg @ ( v_H @ c_Message_Oparts @ ( A @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(simp,[status(thm)],[60]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__analz_0) ).
thf(31,plain,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_Message_Oparts @ c_union ) ) @ ( tc_Message_Omsg @ ( C @ ( A @ c_insert ) ) @ c_Message_Oparts @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__insert__subset__Un_0) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Message_Omsg @ tc_set @ ( tc_Message_Omsg @ ( C @ c_Message_Oparts @ ( B @ c_Message_Oparts @ c_union ) ) @ ( tc_Message_Omsg @ ( C @ ( A @ c_insert ) ) @ c_Message_Oparts @ c_lessequals ) ) )
| ~ ( tc_Message_Omsg @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(32,plain,
! [A: $i] :
( ( A @ c_Message_Oanalz @ c_Message_Oparts )
= ( A @ c_Message_Oparts ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(78,plain,
! [A: $i] :
( ( ( A @ c_Message_Oanalz @ c_Message_Oparts )
!= ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) @ c_Message_Oparts ) )
| ( tc_nat @ ( A @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,20]) ).
thf(81,plain,
! [A: $i] :
( ( ( A @ c_Message_Oanalz )
!= ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) ) )
| ( tc_nat @ ( A @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[78]) ).
thf(230,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( tc_nat @ ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true
| ( ( A @ c_Message_Oanalz )
!= ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[81,24]) ).
thf(231,plain,
! [A: $i] :
( ( ( tc_nat @ ( A @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( tc_nat @ ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ( ( A @ c_Message_Oanalz )
!= ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) ) ) ),
inference(simp,[status(thm)],[230]) ).
thf(232,plain,
( ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oanalz )
!= ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) ) ),
inference(pattern_uni,[status(thm)],[231:[bind(A,$thf( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) ))]]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_0) ).
thf(37,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ~ ( D @ ( D @ ( C @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(119,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Message_Oanalz @ c_Message_Oparts )
!= ( B @ c_Message_Oparts ) )
| ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( B @ c_Message_Oanalz @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,55]) ).
thf(120,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[119:[bind(A,$thf( C )),bind(B,$thf( C @ c_Message_Oanalz ))]]) ).
thf(124,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Message_Oanalz @ c_Message_Oparts )
!= ( B @ c_Message_Oparts ) )
| ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( B @ c_Message_Oanalz @ c_Message_Oanalz @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,124]) ).
thf(171,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_Message_Oanalz @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[170:[bind(A,$thf( C )),bind(B,$thf( C @ c_Message_Oanalz ))]]) ).
thf(175,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_Message_Oanalz @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(simp,[status(thm)],[171]) ).
thf(184,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Message_Oanalz @ c_Message_Oparts )
!= ( B @ c_Message_Oparts ) )
| ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( B @ c_Message_Oanalz @ c_Message_Oanalz @ c_Message_Oanalz @ c_lessequals ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,175]) ).
thf(185,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_Message_Oanalz @ c_Message_Oanalz @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[184:[bind(A,$thf( C )),bind(B,$thf( C @ c_Message_Oanalz ))]]) ).
thf(189,plain,
! [A: $i] : ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_Message_Oanalz @ c_Message_Oanalz @ c_Message_Oanalz @ c_lessequals ) ) ),
inference(simp,[status(thm)],[185]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( A
= ( A @ ( B @ v_sko__uhi ) @ c_Message_OinvKey ) )
| ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_1) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( A
= ( A @ ( B @ v_sko__uhi ) @ c_Message_OinvKey ) )
| ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(2,negated_conjecture,
tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(21,plain,
tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(77,plain,
! [A: $i] :
( ( ( A @ c_Message_Oanalz @ c_Message_Oparts )
!= ( v_H @ c_Message_Oparts ) )
| ~ ( tc_Message_Omsg @ ( A @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,25]) ).
thf(80,plain,
! [A: $i] :
( ( ( A @ c_Message_Oanalz )
!= v_H )
| ~ ( tc_Message_Omsg @ ( A @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(126,plain,
! [A: $i] :
( ( ( tc_Message_Omsg @ ( A @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) )
| ( ( A @ c_Message_Oanalz )
!= v_H )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21,80]) ).
thf(127,plain,
! [A: $i] :
( ( ( tc_Message_Omsg @ ( A @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) )
| ( ( A @ c_Message_Oanalz )
!= v_H ) ),
inference(simp,[status(thm)],[126]) ).
thf(133,plain,
! [A: $i] :
( ( tc_Message_Omsg != tc_Message_Omsg )
| ( ( A @ c_Message_Oparts )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey )
!= v_X )
| ( ( A @ c_Message_Oanalz )
!= v_H ) ),
inference(simp,[status(thm)],[127]) ).
thf(137,plain,
! [A: $i] :
( ( ( A @ c_Message_Oparts )
!= ( v_H @ c_Message_Oanalz @ c_Message_Osynth ) )
| ( ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey )
!= v_X )
| ( ( A @ c_Message_Oanalz )
!= v_H ) ),
inference(simp,[status(thm)],[133]) ).
thf(94,plain,
( ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oparts )
!= ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) @ c_Message_Oparts ) ),
inference(simp,[status(thm)],[73]) ).
thf(104,plain,
! [A: $i] :
( ( ( A @ c_Message_Oanalz @ c_Message_Oparts )
!= ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oparts ) )
| ( ( A @ c_Message_Oparts )
!= ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) @ c_Message_Oparts ) ) ),
inference(paramod_ordered,[status(thm)],[32,94]) ).
thf(107,plain,
! [A: $i] :
( ( ( A @ c_Message_Oanalz )
!= ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) ) )
| ( A
!= ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(109,plain,
( ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) )
!= ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) @ c_Message_Oanalz ) ),
inference(simp,[status(thm)],[107]) ).
thf(172,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_Message_Oanalz @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) )
| ( tc_nat @ tc_set @ ( C @ c_Message_OkeysFor @ ( B @ c_Message_OkeysFor @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[124,27]) ).
thf(173,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_Message_Oanalz @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) )
| ( tc_nat @ tc_set @ ( C @ c_Message_OkeysFor @ ( B @ c_Message_OkeysFor @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[172]) ).
thf(174,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( A @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_Message_Oanalz @ c_Message_Oanalz @ c_Message_OkeysFor @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[173:[bind(A,$thf( F )),bind(B,$thf( F @ c_Message_Oanalz @ c_Message_Oanalz )),bind(C,$thf( F @ c_Message_Oparts ))]]) ).
thf(176,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( A @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_Message_Oanalz @ c_Message_Oanalz @ c_Message_OkeysFor @ c_lessequals ) ) ),
inference(simp,[status(thm)],[174]) ).
thf(56,plain,
( ( ( tc_Message_Omsg @ ( v_H @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21,25]) ).
thf(57,plain,
( ( tc_Message_Omsg @ ( v_H @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(58,plain,
( ( tc_Message_Omsg != tc_Message_Omsg )
| ( ( v_H @ c_Message_Oanalz @ c_Message_Osynth )
!= ( v_H @ c_Message_Oparts ) )
| ( ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey )
!= v_X ) ),
inference(simp,[status(thm)],[57]) ).
thf(59,plain,
( ( ( v_H @ c_Message_Oanalz @ c_Message_Osynth )
!= ( v_H @ c_Message_Oparts ) )
| ( ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey )
!= v_X ) ),
inference(simp,[status(thm)],[58]) ).
thf(67,plain,
( ( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) )
!= ( tc_nat @ ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21,24]) ).
thf(68,plain,
( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) )
!= ( tc_nat @ ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[67]) ).
thf(71,plain,
( ( tc_nat != tc_Message_Omsg )
| ( ( v_H @ c_Message_Oanalz @ c_Message_Osynth )
!= ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oparts @ c_Message_OkeysFor ) )
| ( v_X != v_K ) ),
inference(simp,[status(thm)],[68]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ ( B @ v_sko__uhi ) @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Event_OkeysFor__synth_H_0) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ ( B @ v_sko__uhi ) @ c_Message_Omsg_OKey @ c_in ) ) )
| ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUn__iff_2) ).
thf(39,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( D @ c_union ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(103,plain,
( ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) )
!= ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(64,plain,
( ( ( tc_nat @ ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,25]) ).
thf(65,plain,
( ( tc_nat @ ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(simp,[status(thm)],[64]) ).
thf(66,plain,
( ( tc_nat != tc_Message_Omsg )
| ( ( tc_Message_Omsg @ ( v_G @ ( v_X @ c_insert ) ) @ c_Message_Oparts @ c_Message_OkeysFor )
!= ( v_H @ c_Message_Oparts ) )
| ( ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey )
!= v_K ) ),
inference(simp,[status(thm)],[65]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oanalz__conj__parts_0) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_in ) ) )
| ~ ( tc_Message_Omsg @ ( B @ c_Message_Oanalz @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
thf(43,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ tc_set @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(74,plain,
! [A: $i] :
( ( ( A @ c_Message_OinvKey @ c_Message_OinvKey )
!= ( v_K @ c_Message_OinvKey ) )
| ( ( v_H @ c_Message_Oanalz @ c_Message_Osynth )
!= ( v_H @ c_Message_Oparts ) )
| ( ( A @ c_Message_Omsg_OKey )
!= v_X ) ),
inference(paramod_ordered,[status(thm)],[46,59]) ).
thf(75,plain,
! [A: $i] :
( ( ( A @ c_Message_OinvKey )
!= v_K )
| ( ( v_H @ c_Message_Oanalz @ c_Message_Osynth )
!= ( v_H @ c_Message_Oparts ) )
| ( ( A @ c_Message_Omsg_OKey )
!= v_X ) ),
inference(simp,[status(thm)],[74]) ).
thf(247,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) )
!= ( C @ ( B @ ( A @ c_in ) ) ) )
| ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21,34]) ).
thf(248,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ ( v_X @ c_in ) ) )
!= ( C @ ( B @ ( A @ c_in ) ) ) )
| ( C @ ( C @ ( D @ ( B @ c_union ) ) @ ( A @ c_in ) ) ) ),
inference(simp,[status(thm)],[247]) ).
thf(249,plain,
! [A: $i] : ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) @ ( v_X @ c_in ) ) ),
inference(pattern_uni,[status(thm)],[248:[bind(A,$thf( v_X )),bind(B,$thf( v_H @ c_Message_Oanalz @ c_Message_Osynth )),bind(C,$thf( tc_Message_Omsg )),bind(D,$thf( D ))]]) ).
thf(287,plain,
! [A: $i] : ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) @ ( v_X @ c_in ) ) ),
inference(simp,[status(thm)],[249]) ).
thf(299,plain,
! [A: $i] :
( ( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) @ ( v_X @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[287,25]) ).
thf(300,plain,
! [A: $i] :
( ( tc_Message_Omsg @ ( tc_Message_Omsg @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) @ ( v_X @ c_in ) ) )
!= ( tc_Message_Omsg @ ( v_H @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(simp,[status(thm)],[299]) ).
thf(308,plain,
! [A: $i] :
( ( tc_Message_Omsg != tc_Message_Omsg )
| ( ( tc_Message_Omsg @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) )
!= ( v_H @ c_Message_Oparts ) )
| ( ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey )
!= v_X ) ),
inference(simp,[status(thm)],[300]) ).
thf(315,plain,
! [A: $i] :
( ( ( tc_Message_Omsg @ ( A @ ( v_H @ c_Message_Oanalz @ c_Message_Osynth @ c_union ) ) )
!= ( v_H @ c_Message_Oparts ) )
| ( ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey )
!= v_X ) ),
inference(simp,[status(thm)],[308]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( A
= ( A @ ( B @ v_sko__uhi ) @ c_Message_OinvKey ) )
| ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) ) ),
inference(cnf,[status(esa)],[28]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ c_Message_OkeysFor @ ( A @ c_in ) ) )
| ~ ( tc_nat @ ( B @ c_Message_Osynth @ c_Message_OkeysFor @ ( A @ c_in ) ) )
| ( ( A @ ( B @ v_sko__uhi ) @ c_Message_OinvKey )
= A ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(17,axiom,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_union ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Message_Oparts__Un_0) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( tc_Message_Omsg @ ( B @ ( A @ c_union ) ) @ c_Message_Oparts )
= ( tc_Message_Omsg @ ( B @ c_Message_Oparts @ ( A @ c_Message_Oparts @ c_union ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(186,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_Message_Oanalz @ c_Message_Oanalz @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) )
| ( tc_nat @ tc_set @ ( C @ c_Message_OkeysFor @ ( B @ c_Message_OkeysFor @ c_lessequals ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[175,27]) ).
thf(187,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_Message_Omsg @ tc_set @ ( A @ c_Message_Oparts @ ( A @ c_Message_Oanalz @ c_Message_Oanalz @ c_Message_Oanalz @ c_lessequals ) ) )
!= ( tc_Message_Omsg @ tc_set @ ( C @ ( B @ c_lessequals ) ) ) )
| ( tc_nat @ tc_set @ ( C @ c_Message_OkeysFor @ ( B @ c_Message_OkeysFor @ c_lessequals ) ) ) ),
inference(simp,[status(thm)],[186]) ).
thf(188,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( A @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_Message_Oanalz @ c_Message_Oanalz @ c_Message_Oanalz @ c_Message_OkeysFor @ c_lessequals ) ) ),
inference(pattern_uni,[status(thm)],[187:[bind(A,$thf( G )),bind(B,$thf( G @ c_Message_Oanalz @ c_Message_Oanalz @ c_Message_Oanalz )),bind(C,$thf( G @ c_Message_Oparts ))]]) ).
thf(190,plain,
! [A: $i] : ( tc_nat @ tc_set @ ( A @ c_Message_Oparts @ c_Message_OkeysFor @ ( A @ c_Message_Oanalz @ c_Message_Oanalz @ c_Message_Oanalz @ c_Message_OkeysFor @ c_lessequals ) ) ),
inference(simp,[status(thm)],[188]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Message_Oanalz @ c_Message_Oparts )
!= ( B @ c_Message_Oparts ) )
| ( ( B @ c_Message_Oanalz )
!= v_H )
| ~ ( tc_Message_Omsg @ ( A @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,80]) ).
thf(129,plain,
! [A: $i] :
( ( ( A @ c_Message_Oanalz @ c_Message_Oanalz )
!= v_H )
| ~ ( tc_Message_Omsg @ ( A @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(pattern_uni,[status(thm)],[128:[bind(A,$thf( C )),bind(B,$thf( C @ c_Message_Oanalz ))]]) ).
thf(136,plain,
! [A: $i] :
( ( ( A @ c_Message_Oanalz @ c_Message_Oanalz )
!= v_H )
| ~ ( tc_Message_Omsg @ ( A @ c_Message_Oparts @ ( v_K @ c_Message_OinvKey @ c_Message_Omsg_OKey @ c_in ) ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(76,plain,
! [A: $i] :
( ( ( A @ c_Message_Oanalz @ c_Message_Oparts )
!= ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) @ c_Message_Oparts ) )
| ~ ( tc_nat @ ( A @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,24]) ).
thf(79,plain,
! [A: $i] :
( ( ( A @ c_Message_Oanalz )
!= ( tc_Message_Omsg @ ( v_H @ ( v_G @ c_union ) ) ) )
| ~ ( tc_nat @ ( A @ c_Message_Oparts @ c_Message_OkeysFor @ ( v_K @ c_in ) ) ) ),
inference(simp,[status(thm)],[76]) ).
thf(753,plain,
$false,
inference(e,[status(thm)],[347,125,53,41,73,63,31,47,232,24,288,37,25,189,20,46,28,33,21,137,109,124,45,32,34,176,22,59,27,71,49,81,39,103,66,80,35,175,43,26,55,23,75,287,315,30,51,190,136,79,94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV276-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.07/0.63 % Computer : n015.cluster.edu
% 0.07/0.63 % Model : x86_64 x86_64
% 0.07/0.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.63 % Memory : 8046.5625MB
% 0.07/0.63 % OS : Linux 6.8.0-71-generic
% 0.07/0.63 % CPULimit : 300
% 0.07/0.63 % WCLimit : 300
% 0.07/0.63 % DateTime : Sat Sep 26 13:29:14 UTC 2026
% 0.07/0.63 % CPUTime :
% 0.07/0.63 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.01/1.20 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.40/1.40 % [INFO] Parsing done (191ms).
% 1.40/1.41 % [INFO] Running in sequential loop mode.
% 2.07/1.81 % [INFO] eprover registered as external prover.
% 2.07/1.82 % [INFO] Scanning for conjecture ...
% 2.26/1.93 % [INFO] Found a conjecture (or negated_conjecture) and 15 axioms. Running axiom selection ...
% 2.26/1.99 % [INFO] Axiom selection finished. Selected 15 axioms (removed 0 axioms).
% 2.26/2.03 % [INFO] Problem is propositional (TPTP CNF).
% 2.26/2.03 % [INFO] Type checking passed.
% 2.26/2.04 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 12.56/4.36 % External prover 'e' found a proof!
% 12.56/4.36 % [INFO] Killing All external provers ...
% 12.56/4.36 % Time passed: 3590ms (effective reasoning time: 2943ms)
% 12.56/4.36 % Axioms used in derivation (15): cls_Message_OkeysFor__Un_0, cls_Message_Oanalz__conj__parts_0, cls_Message_Oparts__synth_0, cls_Set_OUn__iff_0, cls_Set_OsubsetD_0, cls_Set_OUn__iff_1, cls_Message_Oanalz__subset__parts_0, cls_Event_OkeysFor__synth_H_1, cls_Message_Oparts__analz_0, cls_Message_OinvKey_A_IinvKey_Ay_J_A_61_61_Ay_0, cls_Message_Oparts__insert__subset__Un_0, cls_Event_OkeysFor__synth_H_0, cls_Message_Oparts__Un_0, cls_Set_OUn__iff_2, cls_Message_OkeysFor__mono_0
% 12.56/4.36 % No. of inferences in proof: 123
% 12.56/4.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3590 ms resp. 2943 ms w/o parsing
% 11.37/4.45 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.37/4.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------