TSTP Solution File: SWW387+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW387+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 20:58:28 EDT 2022
% Result : Theorem 6.70s 4.99s
% Output : Proof 7.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 46
% Syntax : Number of formulae : 80 ( 22 unt; 23 typ; 0 def)
% Number of atoms : 258 ( 56 equ)
% Maximal formula atoms : 8 ( 4 avg)
% Number of connectives : 251 ( 93 ~; 94 |; 0 &)
% ( 40 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 43 ( 43 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 10 >; 5 *; 0 +; 0 <<)
% Number of predicates : 14 ( 11 usr; 4 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 11 con; 0-2 aty)
% Number of variables : 62 ( 54 !; 0 ?; 62 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_Option_Ooption_ONone_type,type,
c_Option_Ooption_ONone: $i > $i ).
tff(tc_Com_Ocom_type,type,
tc_Com_Ocom: $i ).
tff(hAPP_type,type,
hAPP: ( $i * $i ) > $i ).
tff(v_y_type,type,
v_y: $i ).
tff(c_Option_Ooption_OSome_type,type,
c_Option_Ooption_OSome: $i > $i ).
tff(v_pn_type,type,
v_pn: $i ).
tff(c_Com_Obodies_type,type,
c_Com_Obodies: $i ).
tff(c_Map_Omap__of_type,type,
c_Map_Omap__of: ( $i * $i ) > $i ).
tff(tc_Com_Opname_type,type,
tc_Com_Opname: $i ).
tff(c_Com_Obody_type,type,
c_Com_Obody: $i ).
tff(hBOOL_type,type,
hBOOL: $i > $o ).
tff(c_Com_Ocom_OBODY_type,type,
c_Com_Ocom_OBODY: $i ).
tff(c_Com_OWT_type,type,
c_Com_OWT: $i ).
tff(c_Hoare__Mirabelle_Ohoare__derivs_type,type,
c_Hoare__Mirabelle_Ohoare__derivs: ( $i * $i * $i ) > $o ).
tff(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
tff(tc_fun_type,type,
tc_fun: ( $i * $i ) > $i ).
tff(tc_HOL_Obool_type,type,
tc_HOL_Obool: $i ).
tff(tc_Hoare__Mirabelle_Otriple_type,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
tff(tc_Com_Ostate_type,type,
tc_Com_Ostate: $i ).
tff(c_Hoare__Mirabelle_OMGT_type,type,
c_Hoare__Mirabelle_OMGT: $i ).
tff(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i ).
tff(c_Hoare__Mirabelle_Ostate__not__singleton_type,type,
c_Hoare__Mirabelle_Ostate__not__singleton: $o ).
tff(c_Com_OWT__bodies_type,type,
c_Com_OWT__bodies: $o ).
tff(1,plain,
( ( hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) )
<=> ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) )
<=> ( hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
tff(4,plain,
hAPP(c_Com_Obody,v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),v_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) = hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),v_pn),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( ( hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) = c_Option_Ooption_ONone(tc_Com_Ocom) )
<=> ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) )
<=> ( hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
( ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
<=> ~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ),
inference(rewrite,[status(thm)],]) ).
tff(10,axiom,
~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).
tff(11,plain,
~ c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))),
inference(modus_ponens,[status(thm)],[10,9]) ).
tff(12,plain,
^ [V_ca_2: $i] :
refl(
( ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2)) )
<=> ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [V_ca_2: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2)) )
<=> ! [V_ca_2: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [V_ca_2: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2)) )
<=> ! [V_ca_2: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
^ [V_ca_2: $i] :
trans(
monotonicity(
trans(
monotonicity(
iff_true(asserted(c_Com_OWT__bodies),
( c_Com_OWT__bodies
<=> $true )),
( ~ c_Com_OWT__bodies
<=> ~ $true )),
rewrite(
( ~ $true
<=> $false )),
( ~ c_Com_OWT__bodies
<=> $false )),
trans(
monotonicity(
iff_true(asserted(c_Hoare__Mirabelle_Ostate__not__singleton),
( c_Hoare__Mirabelle_Ostate__not__singleton
<=> $true )),
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
<=> ~ $true )),
rewrite(
( ~ $true
<=> $false )),
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
<=> $false )),
( ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2))
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
<=> ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2))
| $false
| $false ) )),
rewrite(
( ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2))
| $false
| $false )
<=> ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) )),
( ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2))
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
<=> ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [V_ca_2: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2))
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton )
<=> ! [V_ca_2: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2)) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
^ [V_ca_2: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( hBOOL(hAPP(c_Com_OWT,V_ca_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) )
<=> ( ~ hBOOL(hAPP(c_Com_OWT,V_ca_2))
| c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) )),
( ( c_Com_OWT__bodies
=> ( hBOOL(hAPP(c_Com_OWT,V_ca_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) )
<=> ( c_Com_OWT__bodies
=> ( ~ hBOOL(hAPP(c_Com_OWT,V_ca_2))
| c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) )),
rewrite(
( ( c_Com_OWT__bodies
=> ( ~ hBOOL(hAPP(c_Com_OWT,V_ca_2))
| c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) )
<=> ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2))
| ~ c_Com_OWT__bodies ) )),
( ( c_Com_OWT__bodies
=> ( hBOOL(hAPP(c_Com_OWT,V_ca_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) )
<=> ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2))
| ~ c_Com_OWT__bodies ) )),
( ( c_Hoare__Mirabelle_Ostate__not__singleton
=> ( c_Com_OWT__bodies
=> ( hBOOL(hAPP(c_Com_OWT,V_ca_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) )
<=> ( c_Hoare__Mirabelle_Ostate__not__singleton
=> ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2))
| ~ c_Com_OWT__bodies ) ) )),
rewrite(
( ( c_Hoare__Mirabelle_Ostate__not__singleton
=> ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2))
| ~ c_Com_OWT__bodies ) )
<=> ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2))
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ) )),
( ( c_Hoare__Mirabelle_Ostate__not__singleton
=> ( c_Com_OWT__bodies
=> ( hBOOL(hAPP(c_Com_OWT,V_ca_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) )
<=> ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2))
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ) )),
inference(bind,[status(th)],]) ).
tff(18,plain,
( ! [V_ca_2: $i] :
( c_Hoare__Mirabelle_Ostate__not__singleton
=> ( c_Com_OWT__bodies
=> ( hBOOL(hAPP(c_Com_OWT,V_ca_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) )
<=> ! [V_ca_2: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2))
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,axiom,
! [V_ca_2: $i] :
( c_Hoare__Mirabelle_Ostate__not__singleton
=> ( c_Com_OWT__bodies
=> ( hBOOL(hAPP(c_Com_OWT,V_ca_2))
=> c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_MGF) ).
tff(20,plain,
! [V_ca_2: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2))
| ~ c_Com_OWT__bodies
| ~ c_Hoare__Mirabelle_Ostate__not__singleton ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [V_ca_2: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2)) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
! [V_ca_2: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2)) ),
inference(modus_ponens,[status(thm)],[21,14]) ).
tff(23,plain,
! [V_ca_2: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2)) ),
inference(skolemize,[status(sab)],[22]) ).
tff(24,plain,
! [V_ca_2: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2)) ),
inference(modus_ponens,[status(thm)],[23,13]) ).
tff(25,plain,
( ( ~ ! [V_ca_2: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2)) )
| c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,v_pn))) )
<=> ( ~ ! [V_ca_2: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2)) )
| c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,v_pn))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(26,plain,
( ~ ! [V_ca_2: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2)) )
| c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,v_pn))) ),
inference(quant_inst,[status(thm)],]) ).
tff(27,plain,
( ~ ! [V_ca_2: $i] :
( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,V_ca_2)) )
| c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(c_Hoare__Mirabelle_OMGT,hAPP(c_Com_Ocom_OBODY,v_pn))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool))))
| ~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,v_pn))) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
~ hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,v_pn))),
inference(unit_resolution,[status(thm)],[27,24,11]) ).
tff(29,plain,
^ [V_pn: $i] :
refl(
( ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn)))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
<=> ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn)))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn)))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
<=> ! [V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn)))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
^ [V_pn: $i] :
rewrite(
( ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn)))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
<=> ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn)))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn)))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
<=> ! [V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn)))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn)))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
<=> ! [V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn)))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
^ [V_pn: $i] :
rewrite(
( ( ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom) )
=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) )
<=> ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn)))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [V_pn: $i] :
( ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom) )
=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) )
<=> ! [V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn)))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,axiom,
! [V_pn: $i] :
( ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom) )
=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_WT_OBody) ).
tff(37,plain,
! [V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn)))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn)))
| ( hAPP(c_Com_Obody,V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn)))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
inference(modus_ponens,[status(thm)],[38,32]) ).
tff(40,plain,
! [V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn)))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn)))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
inference(modus_ponens,[status(thm)],[40,30]) ).
tff(42,plain,
( ( ~ ! [V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn)))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
| hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,v_pn)))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
<=> ( ~ ! [V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn)))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
| hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,v_pn)))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ~ ! [V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn)))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
| hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,v_pn)))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [V_pn: $i] :
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn)))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),V_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) )
| hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,v_pn)))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,v_pn)))
| ( hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
inference(unit_resolution,[status(thm)],[44,41]) ).
tff(46,plain,
hAPP(hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies),v_pn) = c_Option_Ooption_ONone(tc_Com_Ocom),
inference(unit_resolution,[status(thm)],[45,28]) ).
tff(47,plain,
hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) = c_Option_Ooption_ONone(tc_Com_Ocom),
inference(modus_ponens,[status(thm)],[46,8]) ).
tff(48,plain,
^ [V_a_H: $i,T_a: $i] :
refl(
( ( hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) )
<=> ( hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [V_a_H: $i,T_a: $i] : ( hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) )
<=> ! [V_a_H: $i,T_a: $i] : ( hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [V_a_H: $i,T_a: $i] : ( hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) )
<=> ! [V_a_H: $i,T_a: $i] : ( hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,axiom,
! [V_a_H: $i,T_a: $i] : ( hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_option_Osimps_I3_J) ).
tff(52,plain,
! [V_a_H: $i,T_a: $i] : ( hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [V_a_H: $i,T_a: $i] : ( hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [V_a_H: $i,T_a: $i] : ( hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( ~ ! [V_a_H: $i,T_a: $i] : ( hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) )
| ( hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) != c_Option_Ooption_ONone(tc_Com_Ocom) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),v_y) != c_Option_Ooption_ONone(tc_Com_Ocom),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
$false,
inference(unit_resolution,[status(thm)],[56,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWW387+1 : TPTP v8.1.0. Released v5.2.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n021.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun Sep 4 15:53:46 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 6.70/4.99 % SZS status Theorem
% 6.70/4.99 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------