%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW470^1 : TPTP v9.3.1. Released v5.3.0.
% 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 : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:40:13 AM UTC 2026
% Result : Theorem 25.35s 6.44s
% Output : Refutation 23.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 99
% Syntax : Number of formulae : 241 ( 111 unt; 0 typ; 1 def)
% Number of atoms : 987 ( 303 equ; 6 cnn)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 1831 ( 134 ~; 41 |; 71 &;1366 @)
% ( 0 <=>; 219 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Number of types : 5 ( 4 usr)
% Number of type conns : 413 ( 413 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 25 usr; 7 con; 0-4 aty)
% Number of variables : 713 ( 102 ^; 575 !; 35 ?; 713 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(x_a_type,type,
x_a: $tType ).
thf(com_type,type,
com: $tType ).
thf(state_type,type,
state: $tType ).
thf(hoare_669141180iple_a_type,type,
hoare_669141180iple_a: $tType ).
thf(skip_decl,type,
skip: com ).
thf(semi_decl,type,
semi: com > com > com ).
thf(ex_decl,type,
ex: ( hoare_669141180iple_a > $o ) > $o ).
thf(finite957651855iple_a_decl,type,
finite957651855iple_a: ( hoare_669141180iple_a > $o ) > $o ).
thf(finite840267660iple_a_decl,type,
finite840267660iple_a: ( hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a ) > ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a > $o ).
thf(finite684844060iple_a_decl,type,
finite684844060iple_a: ( hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a ) > ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a ).
thf(finite590756294iple_a_decl,type,
finite590756294iple_a: ( hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a ) > hoare_669141180iple_a > ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a > $o ).
thf(finite972428089iple_a_decl,type,
finite972428089iple_a: ( hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a ) > ( ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a ) > $o ).
thf(finite252461622iple_a_decl,type,
finite252461622iple_a: ( hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a ) > ( ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a ) > $o ).
thf(the_Ho49089901iple_a_decl,type,
the_Ho49089901iple_a: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a ).
thf(hoare_2128652938rivs_a_decl,type,
hoare_2128652938rivs_a: ( hoare_669141180iple_a > $o ) > ( hoare_669141180iple_a > $o ) > $o ).
thf(hoare_1295064928iple_a_decl,type,
hoare_1295064928iple_a: ( x_a > state > $o ) > com > ( x_a > state > $o ) > hoare_669141180iple_a ).
thf(bot_bo280939947le_a_o_decl,type,
bot_bo280939947le_a_o: hoare_669141180iple_a > $o ).
thf(bot_bot_o_decl,type,
bot_bot_o: $o ).
thf(collec1717965009iple_a_decl,type,
collec1717965009iple_a: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a > $o ).
thf(insert175534902iple_a_decl,type,
insert175534902iple_a: hoare_669141180iple_a > ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a > $o ).
thf(the_el738790235iple_a_decl,type,
the_el738790235iple_a: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a ).
thf(fequal182287803iple_a_decl,type,
fequal182287803iple_a: hoare_669141180iple_a > hoare_669141180iple_a > $o ).
thf(member1016246415iple_a_decl,type,
member1016246415iple_a: hoare_669141180iple_a > ( hoare_669141180iple_a > $o ) > $o ).
thf(g_decl,type,
g: hoare_669141180iple_a > $o ).
thf(p_decl,type,
p: x_a > state > $o ).
thf(b_decl,type,
b: state > $o ).
thf(c_decl,type,
c: com ).
thf(sk1_decl,type,
sk1: hoare_669141180iple_a > ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a ).
thf(sk32_decl,type,
sk32: hoare_669141180iple_a ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
@+[C: hoare_669141180iple_a] :
~ ( ( B @ C )
=> ( C = A ) ) ) ) ).
thf(28,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a > $o] :
( ( member1016246415iple_a @ A @ ( insert175534902iple_a @ B @ C ) )
= ( ( A = B )
| ( member1016246415iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_insert__iff) ).
thf(217,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a > $o] :
( ( member1016246415iple_a @ A @ ( insert175534902iple_a @ B @ C ) )
= ( ( A = B )
| ( member1016246415iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(88,axiom,
! [A: hoare_669141180iple_a > $o] : ( hoare_2128652938rivs_a @ A @ bot_bo280939947le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_empty) ).
thf(450,plain,
! [A: hoare_669141180iple_a > $o] : ( hoare_2128652938rivs_a @ A @ bot_bo280939947le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(451,plain,
! [A: hoare_669141180iple_a > $o] : ( hoare_2128652938rivs_a @ A @ bot_bo280939947le_a_o ),
inference(cnf,[status(esa)],[450]) ).
thf(41,axiom,
! [A: hoare_669141180iple_a] :
( ( bot_bo280939947le_a_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_bot__apply) ).
thf(259,plain,
! [A: hoare_669141180iple_a] :
( ( bot_bo280939947le_a_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(260,plain,
! [A: hoare_669141180iple_a] :
( ( bot_bo280939947le_a_o @ A )
= bot_bot_o ),
inference(cnf,[status(esa)],[259]) ).
thf(261,plain,
! [A: hoare_669141180iple_a] :
( ( bot_bo280939947le_a_o @ A )
= bot_bot_o ),
inference(lifteq,[status(thm)],[260]) ).
thf(498,plain,
! [A: hoare_669141180iple_a > $o] :
( hoare_2128652938rivs_a @ A
@ ^ [B: hoare_669141180iple_a] : bot_bot_o ),
inference(rewrite,[status(thm)],[451,261]) ).
thf(29,axiom,
! [A: hoare_669141180iple_a] :
~ ( member1016246415iple_a @ A @ bot_bo280939947le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_empty__iff) ).
thf(220,plain,
! [A: hoare_669141180iple_a] :
~ ( member1016246415iple_a @ A @ bot_bo280939947le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(221,plain,
~ ? [A: hoare_669141180iple_a] : ( member1016246415iple_a @ A @ bot_bo280939947le_a_o ),
inference(miniscope,[status(thm)],[220]) ).
thf(222,plain,
! [A: hoare_669141180iple_a] :
~ ( member1016246415iple_a @ A @ bot_bo280939947le_a_o ),
inference(cnf,[status(esa)],[221]) ).
thf(491,plain,
! [A: hoare_669141180iple_a] :
~ ( member1016246415iple_a @ A
@ ^ [B: hoare_669141180iple_a] : bot_bot_o ),
inference(rewrite,[status(thm)],[222,261]) ).
thf(84,axiom,
! [A: hoare_669141180iple_a] :
( ( bot_bo280939947le_a_o @ A )
= ( member1016246415iple_a @ A @ bot_bo280939947le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_bot__empty__eq) ).
thf(438,plain,
! [A: hoare_669141180iple_a] :
( ( bot_bo280939947le_a_o @ A )
= ( member1016246415iple_a @ A @ bot_bo280939947le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(439,plain,
! [A: hoare_669141180iple_a] :
( ( bot_bo280939947le_a_o @ A )
= ( member1016246415iple_a @ A @ bot_bo280939947le_a_o ) ),
inference(cnf,[status(esa)],[438]) ).
thf(440,plain,
! [A: hoare_669141180iple_a] :
( ( member1016246415iple_a @ A @ bot_bo280939947le_a_o )
= ( bot_bo280939947le_a_o @ A ) ),
inference(lifteq,[status(thm)],[439]) ).
thf(1217,plain,
! [A: hoare_669141180iple_a] :
( ( member1016246415iple_a @ A
@ ^ [B: hoare_669141180iple_a] : bot_bot_o )
= bot_bot_o ),
inference(rewrite,[status(thm)],[440,261]) ).
thf(1218,plain,
~ bot_bot_o,
inference(rewrite,[status(thm)],[491,1217]) ).
thf(1260,plain,
! [A: hoare_669141180iple_a > $o] :
( hoare_2128652938rivs_a @ A
@ ^ [B: hoare_669141180iple_a] : $false ),
inference(rewrite,[status(thm)],[498,1218]) ).
thf(19,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a] :
( ~ ( fequal182287803iple_a @ A @ B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J_) ).
thf(185,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a] :
( ~ ( fequal182287803iple_a @ A @ B )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(93,axiom,
! [A: hoare_669141180iple_a,B: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a,C: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a] :
( ( B
= ( finite684844060iple_a @ C ) )
=> ( ( B @ ( insert175534902iple_a @ A @ bot_bo280939947le_a_o ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_fold1__singleton__def) ).
thf(464,plain,
! [A: hoare_669141180iple_a,B: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a,C: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a] :
( ( B
= ( finite684844060iple_a @ C ) )
=> ( ( B @ ( insert175534902iple_a @ A @ bot_bo280939947le_a_o ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(3,axiom,
! [A: com,B: com] :
( skip
!= ( semi @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_com_Osimps_I12_J) ).
thf(101,plain,
! [A: com,B: com] :
( skip
!= ( semi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(97,axiom,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a > $o,D: hoare_669141180iple_a] :
( ( finite590756294iple_a @ A @ B @ C @ D )
=> ( ~ ( member1016246415iple_a @ B @ C )
=> ( finite840267660iple_a @ A @ ( insert175534902iple_a @ B @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_fold1Set_Ointros) ).
thf(479,plain,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a > $o,D: hoare_669141180iple_a] :
( ( finite590756294iple_a @ A @ B @ C @ D )
=> ( ~ ( member1016246415iple_a @ B @ C )
=> ( finite840267660iple_a @ A @ ( insert175534902iple_a @ B @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(62,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( finite957651855iple_a @ ( insert175534902iple_a @ A @ B ) )
= ( finite957651855iple_a @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_finite__insert) ).
thf(347,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( finite957651855iple_a @ ( insert175534902iple_a @ A @ B ) )
= ( finite957651855iple_a @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(38,axiom,
! [A: hoare_669141180iple_a > $o,B: hoare_669141180iple_a > $o,C: hoare_669141180iple_a > $o] :
( ( hoare_2128652938rivs_a @ B @ C )
=> ( ( hoare_2128652938rivs_a @ A @ B )
=> ( hoare_2128652938rivs_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_cut) ).
thf(249,plain,
! [A: hoare_669141180iple_a > $o,B: hoare_669141180iple_a > $o,C: hoare_669141180iple_a > $o] :
( ( hoare_2128652938rivs_a @ B @ C )
=> ( ( hoare_2128652938rivs_a @ A @ B )
=> ( hoare_2128652938rivs_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(98,axiom,
! [A: hoare_669141180iple_a > $o] :
( ( ? [B: hoare_669141180iple_a] : ( member1016246415iple_a @ B @ A ) )
= ( A != bot_bo280939947le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_ex__in__conv) ).
thf(481,plain,
! [A: hoare_669141180iple_a > $o] :
( ( ? [B: hoare_669141180iple_a] : ( member1016246415iple_a @ B @ A ) )
= ( A != bot_bo280939947le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(64,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( member1016246415iple_a @ A @ B )
=> ( ( insert175534902iple_a @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_insert__absorb) ).
thf(352,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( member1016246415iple_a @ A @ B )
=> ( ( insert175534902iple_a @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(6,axiom,
! [A: hoare_669141180iple_a] :
( ( the_Ho49089901iple_a @ ( fequal182287803iple_a @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_the__sym__eq__trivial) ).
thf(125,plain,
! [A: hoare_669141180iple_a] :
( ( the_Ho49089901iple_a @ ( fequal182287803iple_a @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(12,axiom,
! [A: hoare_669141180iple_a > $o,B: hoare_669141180iple_a > $o] :
( ( finite957651855iple_a
@ ( collec1717965009iple_a
@ ^ [C: hoare_669141180iple_a] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite957651855iple_a @ ( collec1717965009iple_a @ A ) )
& ( finite957651855iple_a @ ( collec1717965009iple_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_finite__Collect__disjI) ).
thf(157,plain,
! [A: hoare_669141180iple_a > $o,B: hoare_669141180iple_a > $o] :
( ( finite957651855iple_a
@ ( collec1717965009iple_a
@ ^ [C: hoare_669141180iple_a] :
( ( A @ C )
| ( B @ C ) ) ) )
= ( ( finite957651855iple_a @ ( collec1717965009iple_a @ A ) )
& ( finite957651855iple_a @ ( collec1717965009iple_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(55,axiom,
! [A: hoare_669141180iple_a > $o,B: x_a > state > $o] : ( hoare_2128652938rivs_a @ A @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ B @ skip @ B ) @ bot_bo280939947le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_hoare__derivs_OSkip) ).
thf(321,plain,
! [A: hoare_669141180iple_a > $o,B: x_a > state > $o] : ( hoare_2128652938rivs_a @ A @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ B @ skip @ B ) @ bot_bo280939947le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(70,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( B = bot_bo280939947le_a_o )
=> ~ ( member1016246415iple_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_equals0D) ).
thf(376,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( B = bot_bo280939947le_a_o )
=> ~ ( member1016246415iple_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(35,axiom,
! [A: x_a > state > $o,B: hoare_669141180iple_a > $o,C: com,D: x_a > state > $o] :
( ! [E: x_a,F: state] :
( ( D @ E @ F )
=> ? [G: x_a > state > $o,H: x_a > state > $o] :
( ( hoare_2128652938rivs_a @ B @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ G @ C @ H ) @ bot_bo280939947le_a_o ) )
& ! [I: state] :
( ! [J: x_a] :
( ( G @ J @ F )
=> ( H @ J @ I ) )
=> ( A @ E @ I ) ) ) )
=> ( hoare_2128652938rivs_a @ B @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ D @ C @ A ) @ bot_bo280939947le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_conseq) ).
thf(238,plain,
! [A: x_a > state > $o,B: hoare_669141180iple_a > $o,C: com,D: x_a > state > $o] :
( ! [E: x_a,F: state] :
( ( D @ E @ F )
=> ? [G: x_a > state > $o,H: x_a > state > $o] :
( ( hoare_2128652938rivs_a @ B @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ G @ C @ H ) @ bot_bo280939947le_a_o ) )
& ! [I: state] :
( ! [J: x_a] :
( ( G @ J @ F )
=> ( H @ J @ I ) )
=> ( A @ E @ I ) ) ) )
=> ( hoare_2128652938rivs_a @ B @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ D @ C @ A ) @ bot_bo280939947le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(8,axiom,
! [A: hoare_669141180iple_a > $o] :
( ( collec1717965009iple_a @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_Collect__def) ).
thf(132,plain,
! [A: hoare_669141180iple_a > $o] :
( ( collec1717965009iple_a @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(76,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a,D: hoare_669141180iple_a] :
( ( ( insert175534902iple_a @ A @ ( insert175534902iple_a @ B @ bot_bo280939947le_a_o ) )
= ( insert175534902iple_a @ C @ ( insert175534902iple_a @ D @ bot_bo280939947le_a_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_doubleton__eq__iff) ).
thf(396,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a,D: hoare_669141180iple_a] :
( ( ( insert175534902iple_a @ A @ ( insert175534902iple_a @ B @ bot_bo280939947le_a_o ) )
= ( insert175534902iple_a @ C @ ( insert175534902iple_a @ D @ bot_bo280939947le_a_o ) ) )
= ( ( ( A = C )
& ( B = D ) )
| ( ( A = D )
& ( B = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(43,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( insert175534902iple_a @ A @ B )
= ( collec1717965009iple_a
@ ^ [C: hoare_669141180iple_a] :
( ( C = A )
| ( member1016246415iple_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_insert__compr__raw) ).
thf(265,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( insert175534902iple_a @ A @ B )
= ( collec1717965009iple_a
@ ^ [C: hoare_669141180iple_a] :
( ( C = A )
| ( member1016246415iple_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(52,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o,C: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,D: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a] :
( ( finite972428089iple_a @ C @ D )
=> ( ( finite957651855iple_a @ B )
=> ( ~ ( member1016246415iple_a @ A @ B )
=> ( ( B != bot_bo280939947le_a_o )
=> ( ( D @ ( insert175534902iple_a @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_folding__one_Oinsert) ).
thf(312,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o,C: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,D: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a] :
( ( finite972428089iple_a @ C @ D )
=> ( ( finite957651855iple_a @ B )
=> ( ~ ( member1016246415iple_a @ A @ B )
=> ( ( B != bot_bo280939947le_a_o )
=> ( ( D @ ( insert175534902iple_a @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(5,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ? [C: hoare_669141180iple_a] :
( ( B @ C )
& ! [D: hoare_669141180iple_a] :
( ( B @ D )
=> ( D = C ) ) )
=> ( ( B @ A )
=> ( ( the_Ho49089901iple_a @ B )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_the1__equality) ).
thf(116,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ? [C: hoare_669141180iple_a] :
( ( B @ C )
& ! [D: hoare_669141180iple_a] :
( ( B @ D )
=> ( D = C ) ) )
=> ( ( B @ A )
=> ( ( the_Ho49089901iple_a @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(36,axiom,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( finite957651855iple_a @ B )
=> ( ( B != bot_bo280939947le_a_o )
=> ( ex @ ( finite840267660iple_a @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_finite__nonempty__imp__fold1Set) ).
thf(243,plain,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( finite957651855iple_a @ B )
=> ( ( B != bot_bo280939947le_a_o )
=> ( ex @ ( finite840267660iple_a @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(89,axiom,
! [A: hoare_669141180iple_a > $o] :
( ( bot_bo280939947le_a_o
= ( collec1717965009iple_a @ A ) )
= ( ! [B: hoare_669141180iple_a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_empty__Collect__eq) ).
thf(452,plain,
! [A: hoare_669141180iple_a > $o] :
( ( bot_bo280939947le_a_o
= ( collec1717965009iple_a @ A ) )
= ( ! [B: hoare_669141180iple_a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(71,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a > $o] :
( ( insert175534902iple_a @ A @ ( insert175534902iple_a @ B @ C ) )
= ( insert175534902iple_a @ B @ ( insert175534902iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_insert__commute) ).
thf(380,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a > $o] :
( ( insert175534902iple_a @ A @ ( insert175534902iple_a @ B @ C ) )
= ( insert175534902iple_a @ B @ ( insert175534902iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(24,axiom,
! [A: hoare_669141180iple_a > $o] :
( ( ( collec1717965009iple_a @ A )
= bot_bo280939947le_a_o )
= ( ! [B: hoare_669141180iple_a] :
~ ( A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Collect__empty__eq) ).
thf(201,plain,
! [A: hoare_669141180iple_a > $o] :
( ( ( collec1717965009iple_a @ A )
= bot_bo280939947le_a_o )
= ( ! [B: hoare_669141180iple_a] :
~ ( A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(13,axiom,
! [A: hoare_669141180iple_a > $o,B: hoare_669141180iple_a] :
( ( A @ B )
=> ( ! [C: hoare_669141180iple_a] :
( ( A @ C )
=> ( C = B ) )
=> ( ( the_Ho49089901iple_a @ A )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_the__equality) ).
thf(160,plain,
! [A: hoare_669141180iple_a > $o,B: hoare_669141180iple_a] :
( ( A @ B )
=> ( ! [C: hoare_669141180iple_a] :
( ( A @ C )
=> ( C = B ) )
=> ( ( the_Ho49089901iple_a @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(81,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( finite957651855iple_a @ B )
=> ( finite957651855iple_a @ ( insert175534902iple_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_finite_OinsertI) ).
thf(429,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( finite957651855iple_a @ B )
=> ( finite957651855iple_a @ ( insert175534902iple_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(46,axiom,
! [A: hoare_669141180iple_a] :
( ( bot_bo280939947le_a_o @ A )
= bot_bot_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_bot__fun__def) ).
thf(275,plain,
! [A: hoare_669141180iple_a] :
( ( bot_bo280939947le_a_o @ A )
= bot_bot_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1255,plain,
! [A: hoare_669141180iple_a] :
~ ( bot_bo280939947le_a_o @ A ),
inference(rewrite,[status(thm)],[261,1218]) ).
thf(49,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( insert175534902iple_a @ A @ ( collec1717965009iple_a @ B ) )
= ( collec1717965009iple_a
@ ^ [C: hoare_669141180iple_a] :
( ( C != A )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_insert__Collect) ).
thf(302,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( insert175534902iple_a @ A @ ( collec1717965009iple_a @ B ) )
= ( collec1717965009iple_a
@ ^ [C: hoare_669141180iple_a] :
( ( C != A )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(92,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o,C: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,D: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a] :
( ( finite252461622iple_a @ C @ D )
=> ( ( finite957651855iple_a @ B )
=> ( ( B != bot_bo280939947le_a_o )
=> ( ( D @ ( insert175534902iple_a @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_folding__one__idem_Oinsert__idem) ).
thf(461,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o,C: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,D: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a] :
( ( finite252461622iple_a @ C @ D )
=> ( ( finite957651855iple_a @ B )
=> ( ( B != bot_bo280939947le_a_o )
=> ( ( D @ ( insert175534902iple_a @ A @ B ) )
= ( C @ A @ ( D @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(32,axiom,
! [A: hoare_669141180iple_a] :
~ ( member1016246415iple_a @ A @ bot_bo280939947le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_emptyE) ).
thf(229,plain,
! [A: hoare_669141180iple_a] :
~ ( member1016246415iple_a @ A @ bot_bo280939947le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(99,axiom,
! [A: com,B: x_a > state > $o,C: hoare_669141180iple_a > $o,D: x_a > state > $o,E: com,F: x_a > state > $o] :
( ( hoare_2128652938rivs_a @ C @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ D @ E @ F ) @ bot_bo280939947le_a_o ) )
=> ( ( hoare_2128652938rivs_a @ C @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ F @ A @ B ) @ bot_bo280939947le_a_o ) )
=> ( hoare_2128652938rivs_a @ C @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ D @ ( semi @ E @ A ) @ B ) @ bot_bo280939947le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_Comp) ).
thf(484,plain,
! [A: com,B: x_a > state > $o,C: hoare_669141180iple_a > $o,D: x_a > state > $o,E: com,F: x_a > state > $o] :
( ( hoare_2128652938rivs_a @ C @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ D @ E @ F ) @ bot_bo280939947le_a_o ) )
=> ( ( hoare_2128652938rivs_a @ C @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ F @ A @ B ) @ bot_bo280939947le_a_o ) )
=> ( hoare_2128652938rivs_a @ C @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ D @ ( semi @ E @ A ) @ B ) @ bot_bo280939947le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(20,axiom,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( finite684844060iple_a @ A @ B )
= ( the_Ho49089901iple_a @ ( finite840267660iple_a @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_fold1__def) ).
thf(188,plain,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( finite684844060iple_a @ A @ B )
= ( the_Ho49089901iple_a @ ( finite840267660iple_a @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(14,axiom,
! [A: hoare_669141180iple_a > $o,B: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,C: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a] :
( ( finite972428089iple_a @ B @ C )
=> ( ( finite957651855iple_a @ A )
=> ( ( C @ A )
= ( finite684844060iple_a @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_folding__one_Oeq__fold) ).
thf(169,plain,
! [A: hoare_669141180iple_a > $o,B: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,C: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a] :
( ( finite972428089iple_a @ B @ C )
=> ( ( finite957651855iple_a @ A )
=> ( ( C @ A )
= ( finite684844060iple_a @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(96,axiom,
! [A: hoare_669141180iple_a > $o,B: hoare_669141180iple_a,C: hoare_669141180iple_a > $o] :
( ~ ( member1016246415iple_a @ B @ C )
=> ( ~ ( member1016246415iple_a @ B @ A )
=> ( ( ( insert175534902iple_a @ B @ C )
= ( insert175534902iple_a @ B @ A ) )
= ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_insert__ident) ).
thf(476,plain,
! [A: hoare_669141180iple_a > $o,B: hoare_669141180iple_a,C: hoare_669141180iple_a > $o] :
( ~ ( member1016246415iple_a @ B @ C )
=> ( ~ ( member1016246415iple_a @ B @ A )
=> ( ( ( insert175534902iple_a @ B @ C )
= ( insert175534902iple_a @ B @ A ) )
= ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(26,axiom,
finite957651855iple_a @ bot_bo280939947le_a_o,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_finite_OemptyI) ).
thf(212,plain,
finite957651855iple_a @ bot_bo280939947le_a_o,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(57,axiom,
! [A: x_a > state > $o,B: com,C: x_a > state > $o,D: x_a > state > $o,E: com,F: x_a > state > $o] :
( ( ( hoare_1295064928iple_a @ A @ B @ C )
= ( hoare_1295064928iple_a @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_triple_Oinject) ).
thf(328,plain,
! [A: x_a > state > $o,B: com,C: x_a > state > $o,D: x_a > state > $o,E: com,F: x_a > state > $o] :
( ( ( hoare_1295064928iple_a @ A @ B @ C )
= ( hoare_1295064928iple_a @ D @ E @ F ) )
= ( ( A = D )
& ( B = E )
& ( C = F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(40,axiom,
! [A: hoare_669141180iple_a > $o] :
( ( finite957651855iple_a @ A )
= ( ( A = bot_bo280939947le_a_o )
| ? [B: hoare_669141180iple_a > $o,C: hoare_669141180iple_a] :
( ( A
= ( insert175534902iple_a @ C @ B ) )
& ( finite957651855iple_a @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_finite_Osimps) ).
thf(256,plain,
! [A: hoare_669141180iple_a > $o] :
( ( finite957651855iple_a @ A )
= ( ( A = bot_bo280939947le_a_o )
| ? [B: hoare_669141180iple_a > $o,C: hoare_669141180iple_a] :
( ( A
= ( insert175534902iple_a @ C @ B ) )
& ( finite957651855iple_a @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(75,axiom,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a > $o,D: hoare_669141180iple_a] :
( ( finite590756294iple_a @ A @ B @ C @ D )
= ( ( ( C = bot_bo280939947le_a_o )
& ( D = B ) )
| ? [E: hoare_669141180iple_a,F: hoare_669141180iple_a > $o,G: hoare_669141180iple_a] :
( ( C
= ( insert175534902iple_a @ E @ F ) )
& ( D
= ( A @ E @ G ) )
& ~ ( member1016246415iple_a @ E @ F )
& ( finite590756294iple_a @ A @ B @ F @ G ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_fold__graph_Osimps) ).
thf(393,plain,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a > $o,D: hoare_669141180iple_a] :
( ( finite590756294iple_a @ A @ B @ C @ D )
= ( ( ( C = bot_bo280939947le_a_o )
& ( D = B ) )
| ? [E: hoare_669141180iple_a,F: hoare_669141180iple_a > $o,G: hoare_669141180iple_a] :
( ( C
= ( insert175534902iple_a @ E @ F ) )
& ( D
= ( A @ E @ G ) )
& ~ ( member1016246415iple_a @ E @ F )
& ( finite590756294iple_a @ A @ B @ F @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(490,plain,
( finite957651855iple_a
@ ^ [A: hoare_669141180iple_a] : bot_bot_o ),
inference(rewrite,[status(thm)],[212,261]) ).
thf(1263,plain,
( finite957651855iple_a
@ ^ [A: hoare_669141180iple_a] : $false ),
inference(rewrite,[status(thm)],[490,1218]) ).
thf(133,plain,
! [A: hoare_669141180iple_a > $o] :
( ( collec1717965009iple_a @ A )
= A ),
inference(cnf,[status(esa)],[132]) ).
thf(134,plain,
! [A: hoare_669141180iple_a > $o] :
( ( collec1717965009iple_a @ A )
= A ),
inference(lifteq,[status(thm)],[133]) ).
thf(7,axiom,
! [A: com,B: com] :
( ( semi @ A @ B )
!= skip ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_com_Osimps_I13_J) ).
thf(128,plain,
! [A: com,B: com] :
( ( semi @ A @ B )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(4,axiom,
! [A: hoare_669141180iple_a > $o] :
( ? [B: hoare_669141180iple_a] :
( ( A @ B )
& ! [C: hoare_669141180iple_a] :
( ( A @ C )
=> ( C = B ) ) )
=> ( A @ ( the_Ho49089901iple_a @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_theI_H) ).
thf(105,plain,
! [A: hoare_669141180iple_a > $o] :
( ? [B: hoare_669141180iple_a] :
( ( A @ B )
& ! [C: hoare_669141180iple_a] :
( ( A @ C )
=> ( C = B ) ) )
=> ( A @ ( the_Ho49089901iple_a @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(67,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( bot_bo280939947le_a_o
!= ( insert175534902iple_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_empty__not__insert) ).
thf(360,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( bot_bo280939947le_a_o
!= ( insert175534902iple_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(17,axiom,
! [A: hoare_669141180iple_a] :
( ( the_Ho49089901iple_a
@ ^ [B: hoare_669141180iple_a] : ( B = A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_the__eq__trivial) ).
thf(180,plain,
! [A: hoare_669141180iple_a] :
( ( the_Ho49089901iple_a
@ ^ [B: hoare_669141180iple_a] : ( B = A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(86,axiom,
! [A: hoare_669141180iple_a] :
( ( collec1717965009iple_a @ ( fequal182287803iple_a @ A ) )
= ( insert175534902iple_a @ A @ bot_bo280939947le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_singleton__conv2) ).
thf(444,plain,
! [A: hoare_669141180iple_a] :
( ( collec1717965009iple_a @ ( fequal182287803iple_a @ A ) )
= ( insert175534902iple_a @ A @ bot_bo280939947le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(16,axiom,
! [A: hoare_669141180iple_a > $o,B: hoare_669141180iple_a > $o] :
( ( ( finite957651855iple_a @ ( collec1717965009iple_a @ B ) )
| ( finite957651855iple_a @ ( collec1717965009iple_a @ A ) ) )
=> ( finite957651855iple_a
@ ( collec1717965009iple_a
@ ^ [C: hoare_669141180iple_a] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_finite__Collect__conjI) ).
thf(176,plain,
! [A: hoare_669141180iple_a > $o,B: hoare_669141180iple_a > $o] :
( ( ( finite957651855iple_a @ ( collec1717965009iple_a @ B ) )
| ( finite957651855iple_a @ ( collec1717965009iple_a @ A ) ) )
=> ( finite957651855iple_a
@ ( collec1717965009iple_a
@ ^ [C: hoare_669141180iple_a] :
( ( B @ C )
& ( A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(80,axiom,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a > $o,D: hoare_669141180iple_a] :
( ( finite840267660iple_a @ A @ ( insert175534902iple_a @ B @ C ) @ D )
=> ~ ! [E: hoare_669141180iple_a,F: hoare_669141180iple_a > $o] :
( ( ( insert175534902iple_a @ B @ C )
= ( insert175534902iple_a @ E @ F ) )
=> ( ( finite590756294iple_a @ A @ E @ F @ D )
=> ( member1016246415iple_a @ E @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_insert__fold1SetE) ).
thf(423,plain,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a > $o,D: hoare_669141180iple_a] :
( ( finite840267660iple_a @ A @ ( insert175534902iple_a @ B @ C ) @ D )
=> ~ ! [E: hoare_669141180iple_a,F: hoare_669141180iple_a > $o] :
( ( ( insert175534902iple_a @ B @ C )
= ( insert175534902iple_a @ E @ F ) )
=> ( ( finite590756294iple_a @ A @ E @ F @ D )
=> ( member1016246415iple_a @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(21,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( member1016246415iple_a @ A @ B )
= ( B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_mem__def) ).
thf(191,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( member1016246415iple_a @ A @ B )
= ( B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(25,axiom,
! [A: hoare_669141180iple_a > $o,B: hoare_669141180iple_a] :
( ( ( A @ B )
=> ( ( collec1717965009iple_a
@ ^ [C: hoare_669141180iple_a] :
( ( C = B )
& ( A @ C ) ) )
= ( insert175534902iple_a @ B @ bot_bo280939947le_a_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec1717965009iple_a
@ ^ [C: hoare_669141180iple_a] :
( ( C = B )
& ( A @ C ) ) )
= bot_bo280939947le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Collect__conv__if) ).
thf(204,plain,
! [A: hoare_669141180iple_a > $o,B: hoare_669141180iple_a] :
( ( ( A @ B )
=> ( ( collec1717965009iple_a
@ ^ [C: hoare_669141180iple_a] :
( ( C = B )
& ( A @ C ) ) )
= ( insert175534902iple_a @ B @ bot_bo280939947le_a_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec1717965009iple_a
@ ^ [C: hoare_669141180iple_a] :
( ( C = B )
& ( A @ C ) ) )
= bot_bo280939947le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1256,plain,
! [A: hoare_669141180iple_a] :
~ ( member1016246415iple_a @ A
@ ^ [B: hoare_669141180iple_a] : $false ),
inference(rewrite,[status(thm)],[1217,1218]) ).
thf(1,conjecture,
( hoare_2128652938rivs_a @ g
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [A: x_a,B: state] : $false
@ c
@ ^ [A: x_a,B: state] :
( ( p @ A @ B )
& ~ ( b @ B ) ) )
@ bot_bo280939947le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( hoare_2128652938rivs_a @ g
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [A: x_a,B: state] : $false
@ c
@ ^ [A: x_a,B: state] :
( ( p @ A @ B )
& ~ ( b @ B ) ) )
@ bot_bo280939947le_a_o ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(100,plain,
~ ( hoare_2128652938rivs_a @ g
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [A: x_a,B: state] : $false
@ c
@ ^ [A: x_a,B: state] :
( ( p @ A @ B )
& ~ ( b @ B ) ) )
@ bot_bo280939947le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(489,plain,
~ ( hoare_2128652938rivs_a @ g
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [A: x_a,B: state] : $false
@ c
@ ^ [A: x_a,B: state] :
( ( p @ A @ B )
& ~ ( b @ B ) ) )
@ ^ [A: hoare_669141180iple_a] : bot_bot_o ) ),
inference(rewrite,[status(thm)],[100,261]) ).
thf(499,plain,
! [A: hoare_669141180iple_a > $o] :
( ~ $true
| ( ( hoare_2128652938rivs_a @ A
@ ^ [B: hoare_669141180iple_a] : bot_bot_o )
!= ( hoare_2128652938rivs_a @ g
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [B: x_a,C: state] : $false
@ c
@ ^ [B: x_a,C: state] :
( ( p @ B @ C )
& ~ ( b @ C ) ) )
@ ^ [B: hoare_669141180iple_a] : bot_bot_o ) ) ) ),
inference(paramod_ordered,[status(thm)],[498,489]) ).
thf(500,plain,
! [A: hoare_669141180iple_a > $o] :
( ( hoare_2128652938rivs_a @ A
@ ^ [B: hoare_669141180iple_a] : bot_bot_o )
!= ( hoare_2128652938rivs_a @ g
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [B: x_a,C: state] : $false
@ c
@ ^ [B: x_a,C: state] :
( ( p @ B @ C )
& ~ ( b @ C ) ) )
@ ^ [B: hoare_669141180iple_a] : bot_bot_o ) ) ),
inference(simp,[status(thm)],[499]) ).
thf(501,plain,
! [A: hoare_669141180iple_a > $o] :
( ( A != g )
| ( ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [B: x_a,C: state] : $false
@ c
@ ^ [B: x_a,C: state] :
( ( p @ B @ C )
& ~ ( b @ C ) ) )
@ ^ [B: hoare_669141180iple_a] : bot_bot_o )
!= ( ^ [B: hoare_669141180iple_a] : bot_bot_o ) ) ),
inference(simp,[status(thm)],[500]) ).
thf(502,plain,
( ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [A: x_a,B: state] : $false
@ c
@ ^ [A: x_a,B: state] :
( ( p @ A @ B )
& ~ ( b @ B ) ) )
@ ^ [A: hoare_669141180iple_a] : bot_bot_o )
!= ( ^ [A: hoare_669141180iple_a] : bot_bot_o ) ),
inference(simp,[status(thm)],[501]) ).
thf(503,plain,
( ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [A: x_a,B: state] : $false
@ c
@ ^ [A: x_a,B: state] :
( ( p @ A @ B )
& ~ ( b @ B ) ) )
@ ^ [A: hoare_669141180iple_a] : bot_bot_o
@ sk32 )
!= bot_bot_o ),
inference(func_ext,[status(esa)],[502]) ).
thf(1258,plain,
( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [A: x_a,B: state] : $false
@ c
@ ^ [A: x_a,B: state] :
( ( p @ A @ B )
& ~ ( b @ B ) ) )
@ ^ [A: hoare_669141180iple_a] : $false
@ sk32 ),
inference(rewrite,[status(thm)],[503,1218]) ).
thf(63,axiom,
( bot_bo280939947le_a_o
= ( collec1717965009iple_a
@ ^ [A: hoare_669141180iple_a] : $false ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_empty__def) ).
thf(350,plain,
( bot_bo280939947le_a_o
= ( collec1717965009iple_a
@ ^ [A: hoare_669141180iple_a] : $false ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(15,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a] :
( ( A != B )
| ( fequal182287803iple_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J_) ).
thf(172,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a] :
( ( A != B )
| ( fequal182287803iple_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(106,plain,
! [B: hoare_669141180iple_a,A: hoare_669141180iple_a > $o] :
( ( ~ ( A @ B )
| ( A @ ( sk1 @ B @ A ) )
| ( A @ ( the_Ho49089901iple_a @ A ) ) )
& ( ~ ( A @ B )
| ( ( sk1 @ B @ A )
!= B )
| ( A @ ( the_Ho49089901iple_a @ A ) ) ) ),
inference(cnf,[status(esa)],[105]) ).
thf(107,plain,
! [B: hoare_669141180iple_a,A: hoare_669141180iple_a > $o] :
( ~ ( A @ B )
| ( A @ ( sk1 @ B @ A ) )
| ( A @ ( the_Ho49089901iple_a @ A ) ) ),
inference(cnfConj,[status(thm)],[106]) ).
thf(109,plain,
! [A: hoare_669141180iple_a] :
( ( A != A )
| ( A
= ( sk1 @ A @ ( (=) @ hoare_669141180iple_a @ A ) ) )
| ( A
= ( the_Ho49089901iple_a @ ( (=) @ hoare_669141180iple_a @ A ) ) ) ),
inference(replace_leibeq,[status(thm)],[107:[bind(A,$thf( (=) @ hoare_669141180iple_a @ B ))]]) ).
thf(112,plain,
! [A: hoare_669141180iple_a] :
( ( A != A )
| ( ( sk1 @ A @ ( (=) @ hoare_669141180iple_a @ A ) )
= A )
| ( A
= ( the_Ho49089901iple_a @ ( (=) @ hoare_669141180iple_a @ A ) ) ) ),
inference(lifteq,[status(thm)],[109]) ).
thf(113,plain,
! [A: hoare_669141180iple_a] :
( ( ( sk1 @ A @ ( (=) @ hoare_669141180iple_a @ A ) )
= A )
| ( A
= ( the_Ho49089901iple_a @ ( (=) @ hoare_669141180iple_a @ A ) ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(54,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( insert175534902iple_a @ A @ B )
= ( collec1717965009iple_a
@ ^ [C: hoare_669141180iple_a] :
( ( C = A )
| ( member1016246415iple_a @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_insert__compr) ).
thf(318,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( insert175534902iple_a @ A @ B )
= ( collec1717965009iple_a
@ ^ [C: hoare_669141180iple_a] :
( ( C = A )
| ( member1016246415iple_a @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(73,axiom,
! [A: hoare_669141180iple_a > $o,B: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,C: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a] :
( ( finite972428089iple_a @ B @ C )
=> ( ( finite957651855iple_a @ A )
=> ( ( A != bot_bo280939947le_a_o )
=> ( ! [D: hoare_669141180iple_a,E: hoare_669141180iple_a] : ( member1016246415iple_a @ ( B @ D @ E ) @ ( insert175534902iple_a @ D @ ( insert175534902iple_a @ E @ bot_bo280939947le_a_o ) ) )
=> ( member1016246415iple_a @ ( C @ A ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_folding__one_Oclosed) ).
thf(387,plain,
! [A: hoare_669141180iple_a > $o,B: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,C: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a] :
( ( finite972428089iple_a @ B @ C )
=> ( ( finite957651855iple_a @ A )
=> ( ( A != bot_bo280939947le_a_o )
=> ( ! [D: hoare_669141180iple_a,E: hoare_669141180iple_a] : ( member1016246415iple_a @ ( B @ D @ E ) @ ( insert175534902iple_a @ D @ ( insert175534902iple_a @ E @ bot_bo280939947le_a_o ) ) )
=> ( member1016246415iple_a @ ( C @ A ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(56,axiom,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a > $o,C: hoare_669141180iple_a] :
( ( finite840267660iple_a @ A @ B @ C )
=> ( B != bot_bo280939947le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_fold1Set__nonempty) ).
thf(323,plain,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a > $o,C: hoare_669141180iple_a] :
( ( finite840267660iple_a @ A @ B @ C )
=> ( B != bot_bo280939947le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(27,axiom,
! [A: x_a > state > $o,B: hoare_669141180iple_a > $o,C: x_a > state > $o,D: com,E: x_a > state > $o] :
( ( hoare_2128652938rivs_a @ B @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ C @ D @ E ) @ bot_bo280939947le_a_o ) )
=> ( ! [F: x_a,G: state] :
( ( E @ F @ G )
=> ( A @ F @ G ) )
=> ( hoare_2128652938rivs_a @ B @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ C @ D @ A ) @ bot_bo280939947le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_conseq2) ).
thf(213,plain,
! [A: x_a > state > $o,B: hoare_669141180iple_a > $o,C: x_a > state > $o,D: com,E: x_a > state > $o] :
( ( hoare_2128652938rivs_a @ B @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ C @ D @ E ) @ bot_bo280939947le_a_o ) )
=> ( ! [F: x_a,G: state] :
( ( E @ F @ G )
=> ( A @ F @ G ) )
=> ( hoare_2128652938rivs_a @ B @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ C @ D @ A ) @ bot_bo280939947le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(39,axiom,
! [A: x_a > state > $o,B: x_a > state > $o,C: hoare_669141180iple_a > $o,D: x_a > state > $o,E: com,F: x_a > state > $o] :
( ( hoare_2128652938rivs_a @ C @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ D @ E @ F ) @ bot_bo280939947le_a_o ) )
=> ( ! [G: x_a,H: state] :
( ( B @ G @ H )
=> ! [I: state] :
( ! [J: x_a] :
( ( D @ J @ H )
=> ( F @ J @ I ) )
=> ( A @ G @ I ) ) )
=> ( hoare_2128652938rivs_a @ C @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ B @ E @ A ) @ bot_bo280939947le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_conseq12) ).
thf(251,plain,
! [A: x_a > state > $o,B: x_a > state > $o,C: hoare_669141180iple_a > $o,D: x_a > state > $o,E: com,F: x_a > state > $o] :
( ( hoare_2128652938rivs_a @ C @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ D @ E @ F ) @ bot_bo280939947le_a_o ) )
=> ( ! [G: x_a,H: state] :
( ( B @ G @ H )
=> ! [I: state] :
( ! [J: x_a] :
( ( D @ J @ H )
=> ( F @ J @ I ) )
=> ( A @ G @ I ) ) )
=> ( hoare_2128652938rivs_a @ C @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ B @ E @ A ) @ bot_bo280939947le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(23,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o,C: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,D: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a] :
( ( finite252461622iple_a @ C @ D )
=> ( ( finite957651855iple_a @ B )
=> ( ( member1016246415iple_a @ A @ B )
=> ( ( C @ A @ ( D @ B ) )
= ( D @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_folding__one__idem_Oin__idem) ).
thf(198,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o,C: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,D: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a] :
( ( finite252461622iple_a @ C @ D )
=> ( ( finite957651855iple_a @ B )
=> ( ( member1016246415iple_a @ A @ B )
=> ( ( C @ A @ ( D @ B ) )
= ( D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(77,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] : ( member1016246415iple_a @ A @ ( insert175534902iple_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_insertI1) ).
thf(399,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] : ( member1016246415iple_a @ A @ ( insert175534902iple_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(47,axiom,
! [A: ( hoare_669141180iple_a > $o ) > $o,B: hoare_669141180iple_a > $o] :
( ( finite957651855iple_a @ B )
=> ( ( B != bot_bo280939947le_a_o )
=> ( ! [C: hoare_669141180iple_a] : ( A @ ( insert175534902iple_a @ C @ bot_bo280939947le_a_o ) )
=> ( ! [C: hoare_669141180iple_a,D: hoare_669141180iple_a > $o] :
( ( finite957651855iple_a @ D )
=> ( ( D != bot_bo280939947le_a_o )
=> ( ~ ( member1016246415iple_a @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert175534902iple_a @ C @ D ) ) ) ) ) )
=> ( A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_finite__ne__induct) ).
thf(278,plain,
! [A: ( hoare_669141180iple_a > $o ) > $o,B: hoare_669141180iple_a > $o] :
( ( finite957651855iple_a @ B )
=> ( ( B != bot_bo280939947le_a_o )
=> ( ! [C: hoare_669141180iple_a] : ( A @ ( insert175534902iple_a @ C @ bot_bo280939947le_a_o ) )
=> ( ! [C: hoare_669141180iple_a,D: hoare_669141180iple_a > $o] :
( ( finite957651855iple_a @ D )
=> ( ( D != bot_bo280939947le_a_o )
=> ( ~ ( member1016246415iple_a @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert175534902iple_a @ C @ D ) ) ) ) ) )
=> ( A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(90,axiom,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a] :
( ( finite684844060iple_a @ A @ ( insert175534902iple_a @ B @ bot_bo280939947le_a_o ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_fold1__singleton) ).
thf(455,plain,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a] :
( ( finite684844060iple_a @ A @ ( insert175534902iple_a @ B @ bot_bo280939947le_a_o ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(30,axiom,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a] :
( ( finite840267660iple_a @ A @ ( insert175534902iple_a @ B @ bot_bo280939947le_a_o ) @ C )
= ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_fold1Set__sing) ).
thf(223,plain,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a] :
( ( finite840267660iple_a @ A @ ( insert175534902iple_a @ B @ bot_bo280939947le_a_o ) @ C )
= ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(9,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a,C: $o] :
( ( C
=> ( A
= ( the_Ho49089901iple_a
@ ^ [D: hoare_669141180iple_a] :
( ( C
=> ( D = A ) )
& ( ~ C
=> ( D = B ) ) ) ) ) )
& ( ~ C
=> ( B
= ( the_Ho49089901iple_a
@ ^ [D: hoare_669141180iple_a] :
( ( C
=> ( D = A ) )
& ( ~ C
=> ( D = B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_If__def) ).
thf(135,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a,C: $o] :
( ( C
=> ( A
= ( the_Ho49089901iple_a
@ ^ [D: hoare_669141180iple_a] :
( ( C
=> ( D = A ) )
& ( ~ C
=> ( D = B ) ) ) ) ) )
& ( ~ C
=> ( B
= ( the_Ho49089901iple_a
@ ^ [D: hoare_669141180iple_a] :
( ( C
=> ( D = A ) )
& ( ~ C
=> ( D = B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(31,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a > $o] :
( ( member1016246415iple_a @ A @ ( insert175534902iple_a @ B @ C ) )
=> ( ( A != B )
=> ( member1016246415iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_insertE) ).
thf(226,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a > $o] :
( ( member1016246415iple_a @ A @ ( insert175534902iple_a @ B @ C ) )
=> ( ( A != B )
=> ( member1016246415iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(82,axiom,
! [A: hoare_669141180iple_a > $o,B: hoare_669141180iple_a > $o,C: hoare_669141180iple_a] :
( ( hoare_2128652938rivs_a @ B @ ( insert175534902iple_a @ C @ bot_bo280939947le_a_o ) )
=> ( ( hoare_2128652938rivs_a @ B @ A )
=> ( hoare_2128652938rivs_a @ B @ ( insert175534902iple_a @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_hoare__derivs_Oinsert) ).
thf(431,plain,
! [A: hoare_669141180iple_a > $o,B: hoare_669141180iple_a > $o,C: hoare_669141180iple_a] :
( ( hoare_2128652938rivs_a @ B @ ( insert175534902iple_a @ C @ bot_bo280939947le_a_o ) )
=> ( ( hoare_2128652938rivs_a @ B @ A )
=> ( hoare_2128652938rivs_a @ B @ ( insert175534902iple_a @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(95,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a] :
( ( ( insert175534902iple_a @ A @ bot_bo280939947le_a_o )
= ( insert175534902iple_a @ B @ bot_bo280939947le_a_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_singleton__inject) ).
thf(473,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a] :
( ( ( insert175534902iple_a @ A @ bot_bo280939947le_a_o )
= ( insert175534902iple_a @ B @ bot_bo280939947le_a_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(65,axiom,
! [A: hoare_669141180iple_a > $o] :
( ( A != bot_bo280939947le_a_o )
= ( ? [B: hoare_669141180iple_a,C: hoare_669141180iple_a > $o] :
( ( A
= ( insert175534902iple_a @ B @ C ) )
& ~ ( member1016246415iple_a @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_nonempty__iff) ).
thf(355,plain,
! [A: hoare_669141180iple_a > $o] :
( ( A != bot_bo280939947le_a_o )
= ( ? [B: hoare_669141180iple_a,C: hoare_669141180iple_a > $o] :
( ( A
= ( insert175534902iple_a @ B @ C ) )
& ~ ( member1016246415iple_a @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(91,axiom,
! [A: hoare_669141180iple_a > $o] :
( ( the_el738790235iple_a @ A )
= ( the_Ho49089901iple_a
@ ^ [B: hoare_669141180iple_a] :
( A
= ( insert175534902iple_a @ B @ bot_bo280939947le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_the__elem__def) ).
thf(458,plain,
! [A: hoare_669141180iple_a > $o] :
( ( the_el738790235iple_a @ A )
= ( the_Ho49089901iple_a
@ ^ [B: hoare_669141180iple_a] :
( A
= ( insert175534902iple_a @ B @ bot_bo280939947le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(22,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,C: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a] :
( ( finite252461622iple_a @ B @ C )
=> ( ( B @ A @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_folding__one__idem_Oidem) ).
thf(194,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,C: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a] :
( ( finite252461622iple_a @ B @ C )
=> ( ( B @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(181,plain,
! [A: hoare_669141180iple_a] :
( ( the_Ho49089901iple_a
@ ^ [B: hoare_669141180iple_a] : ( B = A ) )
= A ),
inference(cnf,[status(esa)],[180]) ).
thf(182,plain,
! [A: hoare_669141180iple_a] :
( ( the_Ho49089901iple_a
@ ^ [B: hoare_669141180iple_a] : ( B = A ) )
= A ),
inference(lifteq,[status(thm)],[181]) ).
thf(58,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( member1016246415iple_a @ A @ B )
=> ~ ! [C: hoare_669141180iple_a > $o] :
( ( B
= ( insert175534902iple_a @ A @ C ) )
=> ( member1016246415iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_Set_Oset__insert) ).
thf(331,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( member1016246415iple_a @ A @ B )
=> ~ ! [C: hoare_669141180iple_a > $o] :
( ( B
= ( insert175534902iple_a @ A @ C ) )
=> ( member1016246415iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(85,axiom,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a] :
( ( finite590756294iple_a @ A @ B @ bot_bo280939947le_a_o @ C )
=> ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_empty__fold__graphE) ).
thf(441,plain,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a] :
( ( finite590756294iple_a @ A @ B @ bot_bo280939947le_a_o @ C )
=> ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(126,plain,
! [A: hoare_669141180iple_a] :
( ( the_Ho49089901iple_a @ ( fequal182287803iple_a @ A ) )
= A ),
inference(cnf,[status(esa)],[125]) ).
thf(127,plain,
! [A: hoare_669141180iple_a] :
( ( the_Ho49089901iple_a @ ( fequal182287803iple_a @ A ) )
= A ),
inference(lifteq,[status(thm)],[126]) ).
thf(60,axiom,
! [A: hoare_669141180iple_a > $o] :
( ( ! [B: hoare_669141180iple_a] :
~ ( member1016246415iple_a @ B @ A ) )
= ( A = bot_bo280939947le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_all__not__in__conv) ).
thf(338,plain,
! [A: hoare_669141180iple_a > $o] :
( ( ! [B: hoare_669141180iple_a] :
~ ( member1016246415iple_a @ B @ A ) )
= ( A = bot_bo280939947le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(59,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a > $o] :
( ( member1016246415iple_a @ B @ C )
=> ( member1016246415iple_a @ B @ ( insert175534902iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_insertI2) ).
thf(336,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a > $o] :
( ( member1016246415iple_a @ B @ C )
=> ( member1016246415iple_a @ B @ ( insert175534902iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(11,axiom,
! [A: com,B: com,C: com,D: com] :
( ( ( semi @ A @ B )
= ( semi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_com_Osimps_I3_J) ).
thf(154,plain,
! [A: com,B: com,C: com,D: com] :
( ( ( semi @ A @ B )
= ( semi @ C @ D ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(173,plain,
! [B: hoare_669141180iple_a,A: hoare_669141180iple_a] :
( ( A != B )
| ( fequal182287803iple_a @ A @ B ) ),
inference(cnf,[status(esa)],[172]) ).
thf(174,plain,
! [B: hoare_669141180iple_a,A: hoare_669141180iple_a] :
( ( A != B )
| ( fequal182287803iple_a @ A @ B ) ),
inference(lifteq,[status(thm)],[173]) ).
thf(175,plain,
! [A: hoare_669141180iple_a] : ( fequal182287803iple_a @ A @ A ),
inference(simp,[status(thm)],[174]) ).
thf(10,axiom,
! [A: hoare_669141180iple_a > $o,B: hoare_669141180iple_a] :
( ( A @ B )
=> ( ! [C: hoare_669141180iple_a] :
( ( A @ C )
=> ( C = B ) )
=> ( A @ ( the_Ho49089901iple_a @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_theI) ).
thf(143,plain,
! [A: hoare_669141180iple_a > $o,B: hoare_669141180iple_a] :
( ( A @ B )
=> ( ! [C: hoare_669141180iple_a] :
( ( A @ C )
=> ( C = B ) )
=> ( A @ ( the_Ho49089901iple_a @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(102,plain,
~ ? [A: com,B: com] :
( skip
= ( semi @ A @ B ) ),
inference(miniscope,[status(thm)],[101]) ).
thf(103,plain,
! [B: com,A: com] :
( skip
!= ( semi @ A @ B ) ),
inference(cnf,[status(esa)],[102]) ).
thf(104,plain,
! [B: com,A: com] :
( ( semi @ A @ B )
!= skip ),
inference(lifteq,[status(thm)],[103]) ).
thf(69,axiom,
! [A: hoare_669141180iple_a > $o,B: hoare_669141180iple_a] :
( ( ( A @ B )
=> ( ( collec1717965009iple_a
@ ^ [C: hoare_669141180iple_a] :
( ( B = C )
& ( A @ C ) ) )
= ( insert175534902iple_a @ B @ bot_bo280939947le_a_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec1717965009iple_a
@ ^ [C: hoare_669141180iple_a] :
( ( B = C )
& ( A @ C ) ) )
= bot_bo280939947le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Collect__conv__if2) ).
thf(368,plain,
! [A: hoare_669141180iple_a > $o,B: hoare_669141180iple_a] :
( ( ( A @ B )
=> ( ( collec1717965009iple_a
@ ^ [C: hoare_669141180iple_a] :
( ( B = C )
& ( A @ C ) ) )
= ( insert175534902iple_a @ B @ bot_bo280939947le_a_o ) ) )
& ( ~ ( A @ B )
=> ( ( collec1717965009iple_a
@ ^ [C: hoare_669141180iple_a] :
( ( B = C )
& ( A @ C ) ) )
= bot_bo280939947le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(74,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o,C: hoare_669141180iple_a] :
( ( insert175534902iple_a @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_insert__code) ).
thf(390,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o,C: hoare_669141180iple_a] :
( ( insert175534902iple_a @ A @ B @ C )
= ( ( A = C )
| ( B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(78,axiom,
! [A: hoare_669141180iple_a > $o] :
( ! [B: hoare_669141180iple_a] :
~ ( member1016246415iple_a @ B @ A )
=> ( A = bot_bo280939947le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_equals0I) ).
thf(401,plain,
! [A: hoare_669141180iple_a > $o] :
( ! [B: hoare_669141180iple_a] :
~ ( member1016246415iple_a @ B @ A )
=> ( A = bot_bo280939947le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(83,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( member1016246415iple_a @ A @ B )
=> ? [C: hoare_669141180iple_a > $o] :
( ( B
= ( insert175534902iple_a @ A @ C ) )
& ~ ( member1016246415iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_mk__disjoint__insert) ).
thf(433,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( member1016246415iple_a @ A @ B )
=> ? [C: hoare_669141180iple_a > $o] :
( ( B
= ( insert175534902iple_a @ A @ C ) )
& ~ ( member1016246415iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(45,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( insert175534902iple_a @ A @ ( insert175534902iple_a @ A @ B ) )
= ( insert175534902iple_a @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_insert__absorb2) ).
thf(272,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( insert175534902iple_a @ A @ ( insert175534902iple_a @ A @ B ) )
= ( insert175534902iple_a @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(72,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( insert175534902iple_a @ A @ B )
!= bot_bo280939947le_a_o ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_insert__not__empty) ).
thf(383,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > $o] :
( ( insert175534902iple_a @ A @ B )
!= bot_bo280939947le_a_o ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(34,axiom,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a > $o,C: hoare_669141180iple_a] :
( ( finite840267660iple_a @ A @ B @ C )
= ( ? [D: hoare_669141180iple_a,E: hoare_669141180iple_a > $o,F: hoare_669141180iple_a] :
( ( B
= ( insert175534902iple_a @ D @ E ) )
& ( C = F )
& ( finite590756294iple_a @ A @ D @ E @ F )
& ~ ( member1016246415iple_a @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_fold1Set_Osimps) ).
thf(235,plain,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a > $o,C: hoare_669141180iple_a] :
( ( finite840267660iple_a @ A @ B @ C )
= ( ? [D: hoare_669141180iple_a,E: hoare_669141180iple_a > $o,F: hoare_669141180iple_a] :
( ( B
= ( insert175534902iple_a @ D @ E ) )
& ( C = F )
& ( finite590756294iple_a @ A @ D @ E @ F )
& ~ ( member1016246415iple_a @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(37,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a] :
( ( member1016246415iple_a @ A @ ( insert175534902iple_a @ B @ bot_bo280939947le_a_o ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_singletonE) ).
thf(246,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a] :
( ( member1016246415iple_a @ A @ ( insert175534902iple_a @ B @ bot_bo280939947le_a_o ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(48,axiom,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a,D: hoare_669141180iple_a,E: hoare_669141180iple_a > $o] :
( ~ ( member1016246415iple_a @ D @ E )
=> ( ( finite590756294iple_a @ A @ B @ E @ C )
=> ( finite590756294iple_a @ A @ B @ ( insert175534902iple_a @ D @ E ) @ ( A @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_fold__graph_OinsertI) ).
thf(300,plain,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a,D: hoare_669141180iple_a,E: hoare_669141180iple_a > $o] :
( ~ ( member1016246415iple_a @ D @ E )
=> ( ( finite590756294iple_a @ A @ B @ E @ C )
=> ( finite590756294iple_a @ A @ B @ ( insert175534902iple_a @ D @ E ) @ ( A @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(87,axiom,
! [A: hoare_669141180iple_a] :
( ( collec1717965009iple_a
@ ^ [B: hoare_669141180iple_a] : ( B = A ) )
= ( insert175534902iple_a @ A @ bot_bo280939947le_a_o ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_singleton__conv) ).
thf(447,plain,
! [A: hoare_669141180iple_a] :
( ( collec1717965009iple_a
@ ^ [B: hoare_669141180iple_a] : ( B = A ) )
= ( insert175534902iple_a @ A @ bot_bo280939947le_a_o ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(53,axiom,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a] :
~ ( finite840267660iple_a @ A @ bot_bo280939947le_a_o @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_empty__fold1SetE) ).
thf(315,plain,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a] :
~ ( finite840267660iple_a @ A @ bot_bo280939947le_a_o @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(42,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,C: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a] :
( ( finite972428089iple_a @ B @ C )
=> ( ( C @ ( insert175534902iple_a @ A @ bot_bo280939947le_a_o ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_folding__one_Osingleton) ).
thf(262,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,C: ( hoare_669141180iple_a > $o ) > hoare_669141180iple_a] :
( ( finite972428089iple_a @ B @ C )
=> ( ( C @ ( insert175534902iple_a @ A @ bot_bo280939947le_a_o ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(79,axiom,
! [A: ( hoare_669141180iple_a > $o ) > $o,B: hoare_669141180iple_a > $o] :
( ( finite957651855iple_a @ B )
=> ( ( A @ bot_bo280939947le_a_o )
=> ( ! [C: hoare_669141180iple_a,D: hoare_669141180iple_a > $o] :
( ( finite957651855iple_a @ D )
=> ( ~ ( member1016246415iple_a @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert175534902iple_a @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_finite__induct) ).
thf(405,plain,
! [A: ( hoare_669141180iple_a > $o ) > $o,B: hoare_669141180iple_a > $o] :
( ( finite957651855iple_a @ B )
=> ( ( A @ bot_bo280939947le_a_o )
=> ( ! [C: hoare_669141180iple_a,D: hoare_669141180iple_a > $o] :
( ( finite957651855iple_a @ D )
=> ( ~ ( member1016246415iple_a @ C @ D )
=> ( ( A @ D )
=> ( A @ ( insert175534902iple_a @ C @ D ) ) ) ) )
=> ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(18,axiom,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a > $o] :
( ( finite957651855iple_a @ C )
=> ( ex @ ( finite590756294iple_a @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_finite__imp__fold__graph) ).
thf(183,plain,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a > $o] :
( ( finite957651855iple_a @ C )
=> ( ex @ ( finite590756294iple_a @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(50,axiom,
! [A: x_a > state > $o,B: hoare_669141180iple_a > $o,C: x_a > state > $o,D: com,E: x_a > state > $o] :
( ( hoare_2128652938rivs_a @ B @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ C @ D @ E ) @ bot_bo280939947le_a_o ) )
=> ( ! [F: x_a,G: state] :
( ( A @ F @ G )
=> ( C @ F @ G ) )
=> ( hoare_2128652938rivs_a @ B @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ A @ D @ E ) @ bot_bo280939947le_a_o ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_conseq1) ).
thf(305,plain,
! [A: x_a > state > $o,B: hoare_669141180iple_a > $o,C: x_a > state > $o,D: com,E: x_a > state > $o] :
( ( hoare_2128652938rivs_a @ B @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ C @ D @ E ) @ bot_bo280939947le_a_o ) )
=> ( ! [F: x_a,G: state] :
( ( A @ F @ G )
=> ( C @ F @ G ) )
=> ( hoare_2128652938rivs_a @ B @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ A @ D @ E ) @ bot_bo280939947le_a_o ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(61,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a > $o] :
( ( ~ ( member1016246415iple_a @ B @ C )
=> ( B = A ) )
=> ( member1016246415iple_a @ B @ ( insert175534902iple_a @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_insertCI) ).
thf(341,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a,C: hoare_669141180iple_a > $o] :
( ( ~ ( member1016246415iple_a @ B @ C )
=> ( B = A ) )
=> ( member1016246415iple_a @ B @ ( insert175534902iple_a @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(44,axiom,
! [A: hoare_669141180iple_a > $o,B: x_a > state > $o,C: com,D: x_a > state > $o,E: $o] :
( ( E
=> ( hoare_2128652938rivs_a @ A @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ B @ C @ D ) @ bot_bo280939947le_a_o ) ) )
=> ( hoare_2128652938rivs_a @ A
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [F: x_a,G: state] :
( ( B @ F @ G )
& E )
@ C
@ D )
@ bot_bo280939947le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_constant) ).
thf(268,plain,
! [A: hoare_669141180iple_a > $o,B: x_a > state > $o,C: com,D: x_a > state > $o,E: $o] :
( ( E
=> ( hoare_2128652938rivs_a @ A @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ B @ C @ D ) @ bot_bo280939947le_a_o ) ) )
=> ( hoare_2128652938rivs_a @ A
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [F: x_a,G: state] :
( ( B @ F @ G )
& E )
@ C
@ D )
@ bot_bo280939947le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(66,axiom,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a] : ( finite590756294iple_a @ A @ B @ bot_bo280939947le_a_o @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_fold__graph_OemptyI) ).
thf(358,plain,
! [A: hoare_669141180iple_a > hoare_669141180iple_a > hoare_669141180iple_a,B: hoare_669141180iple_a] : ( finite590756294iple_a @ A @ B @ bot_bo280939947le_a_o @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(108,plain,
! [B: hoare_669141180iple_a,A: hoare_669141180iple_a > $o] :
( ~ ( A @ B )
| ( ( sk1 @ B @ A )
!= B )
| ( A @ ( the_Ho49089901iple_a @ A ) ) ),
inference(cnfConj,[status(thm)],[106]) ).
thf(111,plain,
! [B: hoare_669141180iple_a,A: hoare_669141180iple_a > $o] :
( ( ( sk1 @ B @ A )
!= B )
| ~ ( A @ B )
| ( A @ ( the_Ho49089901iple_a @ A ) ) ),
inference(lifteq,[status(thm)],[108]) ).
thf(94,axiom,
! [A: hoare_669141180iple_a > $o,B: com,C: x_a > state > $o,D: x_a > state > $o] :
( ! [E: x_a,F: state] :
( ( D @ E @ F )
=> ( hoare_2128652938rivs_a @ A
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [G: x_a,H: state] : ( H = F )
@ B
@ ^ [G: x_a] : ( C @ E ) )
@ bot_bo280939947le_a_o ) ) )
=> ( hoare_2128652938rivs_a @ A @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ D @ B @ C ) @ bot_bo280939947le_a_o ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_escape) ).
thf(469,plain,
! [A: hoare_669141180iple_a > $o,B: com,C: x_a > state > $o,D: x_a > state > $o] :
( ! [E: x_a,F: state] :
( ( D @ E @ F )
=> ( hoare_2128652938rivs_a @ A
@ ( insert175534902iple_a
@ ( hoare_1295064928iple_a
@ ^ [G: x_a,H: state] : ( H = F )
@ B
@ ^ [G: x_a] : ( C @ E ) )
@ bot_bo280939947le_a_o ) ) )
=> ( hoare_2128652938rivs_a @ A @ ( insert175534902iple_a @ ( hoare_1295064928iple_a @ D @ B @ C ) @ bot_bo280939947le_a_o ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(51,axiom,
! [A: hoare_669141180iple_a] :
( ( the_el738790235iple_a @ ( insert175534902iple_a @ A @ bot_bo280939947le_a_o ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_the__elem__eq) ).
thf(309,plain,
! [A: hoare_669141180iple_a] :
( ( the_el738790235iple_a @ ( insert175534902iple_a @ A @ bot_bo280939947le_a_o ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(68,axiom,
! [A: hoare_669141180iple_a] :
~ ! [B: x_a > state > $o,C: com,D: x_a > state > $o] :
( A
!= ( hoare_1295064928iple_a @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_triple_Oexhaust) ).
thf(364,plain,
! [A: hoare_669141180iple_a] :
~ ! [B: x_a > state > $o,C: com,D: x_a > state > $o] :
( A
!= ( hoare_1295064928iple_a @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(33,axiom,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a] :
( ( member1016246415iple_a @ A @ ( insert175534902iple_a @ B @ bot_bo280939947le_a_o ) )
= ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_singleton__iff) ).
thf(232,plain,
! [A: hoare_669141180iple_a,B: hoare_669141180iple_a] :
( ( member1016246415iple_a @ A @ ( insert175534902iple_a @ B @ bot_bo280939947le_a_o ) )
= ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(2176,plain,
$false,
inference(e,[status(thm)],[217,1260,185,464,101,479,347,249,481,352,125,157,321,376,238,132,396,265,312,116,243,452,380,201,220,160,429,275,1255,302,461,229,484,188,169,476,212,328,256,393,1263,134,128,105,360,180,444,176,423,191,204,1256,259,1258,350,172,113,318,387,323,213,251,198,399,278,455,223,135,226,438,431,473,355,458,194,182,331,441,127,338,1218,336,154,175,143,450,104,368,390,401,433,272,383,235,246,300,447,315,262,405,183,305,107,341,268,358,111,469,309,364,232,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW470^1 : TPTP v9.3.1. Released v5.3.0.
% 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
% 0.09/0.21 % Computer : n020.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 16:05:49 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 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
% 0.86/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.56/1.10 % [INFO] Parsing done (303ms).
% 1.56/1.11 % [INFO] Running in sequential loop mode.
% 2.60/1.50 % [INFO] eprover registered as external prover.
% 2.60/1.51 % [INFO] Scanning for conjecture ...
% 2.78/1.63 % [INFO] Found a conjecture (or negated_conjecture) and 97 axioms. Running axiom selection ...
% 2.97/1.72 % [INFO] Axiom selection finished. Selected 97 axioms (removed 0 axioms).
% 3.26/1.87 % [INFO] Problem is higher-order (TPTP THF).
% 3.26/1.89 % [INFO] Type checking passed.
% 3.26/1.89 % [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 ...
% 25.35/6.44 % External prover 'e' found a proof!
% 25.35/6.44 % [INFO] Killing All external provers ...
% 25.35/6.44 % Time passed: 6083ms (effective reasoning time: 5324ms)
% 25.35/6.44 % Solved by 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)>
% 25.35/6.44 % Axioms used in derivation (97): fact_10_insertCI, fact_41_bot__apply, fact_63_folding__one_Osingleton, fact_57_theI, fact_4_constant, fact_20_ex__in__conv, fact_42_bot__fun__def, fact_23_insert__absorb, fact_54_If__def, fact_60_conseq, fact_67_fold1Set_Ointros, fact_53_the__eq__trivial, fact_65_empty__fold1SetE, fact_75_folding__one_Oeq__fold, fact_6_conseq2, fact_56_the__equality, fact_46_Set_Oset__insert, help_fequal_1_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J_, fact_55_equals0I, fact_3_hoare__derivs_Oinsert, fact_34_singleton__inject, fact_5_escape, fact_80_finite__insert, fact_0_empty, fact_27_insert__iff, fact_92_finite__ne__induct, fact_52_the__sym__eq__trivial, fact_90_fold__graph_Osimps, fact_16_equals0D, fact_44_Comp, fact_15_Collect__conv__if, fact_25_insert__ident, fact_74_Collect__def, fact_87_finite_Osimps, fact_73_mem__def, fact_8_conseq12, fact_2_cut, fact_37_singleton__iff, fact_85_finite__nonempty__imp__fold1Set, fact_50_mk__disjoint__insert, fact_78_fold__graph_OinsertI, fact_38_insert__not__empty, fact_12_singleton__conv2, fact_29_insert__absorb2, fact_48_com_Osimps_I12_J, fact_77_empty__fold__graphE, fact_69_fold1__def, fact_93_folding__one__idem_Oidem, fact_79_finite__Collect__disjI, fact_51_com_Osimps_I3_J, fact_36_doubleton__eq__iff, fact_47_com_Osimps_I13_J, fact_58_the1__equality, fact_91_folding__one__idem_Oinsert__idem, fact_14_Collect__conv__if2, fact_49_the__elem__def, fact_62_fold1Set__sing, fact_18_empty__iff, fact_22_empty__def, fact_68_folding__one_Oinsert, fact_17_Collect__empty__eq, fact_64_bot__empty__eq, fact_70_finite__Collect__conjI, fact_28_insert__commute, fact_1_triple_Oinject, fact_59_theI_H, fact_35_singletonE, fact_19_empty__Collect__eq, fact_31_insert__compr, help_fequal_2_1_fequal_000tc__Hoare____Mirabelle____ghhkfsbqqq__Otriple_It__a_J_, fact_76_fold__graph_OemptyI, fact_13_singleton__conv, fact_33_insert__compr__raw, fact_24_insertI2, fact_86_finite__induct, fact_21_all__not__in__conv, fact_89_fold1Set_Osimps, fact_39_empty__not__insert, fact_11_emptyE, fact_30_insert__Collect, fact_84_insert__fold1SetE, fact_26_insert__code, fact_83_folding__one_Oclosed, fact_45_triple_Oexhaust, fact_40_the__elem__eq, fact_72_finite_OinsertI, fact_43_hoare__derivs_OSkip, fact_66_fold1Set__nonempty, fact_81_fold1__singleton__def, fact_9_insertE, fact_71_finite_OemptyI, fact_32_insertI1, fact_94_folding__one__idem_Oin__idem, fact_88_finite__imp__fold__graph, fact_61_nonempty__iff, fact_82_fold1__singleton, fact_7_conseq1
% 25.35/6.44 % No. of inferences in proof: 240
% 25.35/6.44 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6083 ms resp. 5324 ms w/o parsing
% 23.76/6.61 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 23.76/6.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------