TPTP Problem File: SWW863+1.p
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%------------------------------------------------------------------------------
% File : SWW863+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : reg_allocProof__12__tactictoe_prove_11__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : reg_allocProof__12__tactictoe_prove_11__dep [Kum18]
% Status : CounterSatisfiable
% Rating : 0.00 v8.2.0, 0.33 v8.1.0, 0.50 v7.5.0, 0.60 v7.4.0, 0.33 v7.3.0
% Syntax : Number of formulae : 19 ( 4 unt; 0 def)
% Number of atoms : 63 ( 29 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 48 ( 4 ~; 4 |; 10 &)
% ( 10 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 23 ( 23 usr; 7 con; 0-4 aty)
% Number of variables : 75 ( 73 !; 2 ?)
% SPC : FOF_CSA_RFO_SEQ
% Comments :
%------------------------------------------------------------------------------
fof('HL_TRUTH',axiom,
p__01(s__02(cbool__00,cT__00)) ).
fof('HL_FALSITY',axiom,
~ p__01(s__02(cbool__00,cF__00)) ).
fof('HL_BOOL_CASES',axiom,
! [Vt] :
( s__02(cbool__00,Vt) = s__02(cbool__00,cT__00)
| s__02(cbool__00,Vt) = s__02(cbool__00,cF__00) ) ).
fof('HL_EXT',axiom,
! [V_3f2384,V_3f2380,Vf,Vg] :
( ! [Vx] : s__02(V_3f2380,chapp__02(s__02(cfun__02(V_3f2384,V_3f2380),Vf),s__02(V_3f2384,Vx))) = s__02(V_3f2380,chapp__02(s__02(cfun__02(V_3f2384,V_3f2380),Vg),s__02(V_3f2384,Vx)))
=> s__02(cfun__02(V_3f2384,V_3f2380),Vf) = s__02(cfun__02(V_3f2384,V_3f2380),Vg) ) ).
fof('thm.bool.TRUTH',axiom,
p__01(s__02(cbool__00,cT__00)) ).
fof('thm.bool.IMP_ANTISYM_AX',axiom,
! [V_27t1_27,V_27t2_27] :
( ( p__01(s__02(cbool__00,V_27t1_27))
=> p__01(s__02(cbool__00,V_27t2_27)) )
=> ( ( p__01(s__02(cbool__00,V_27t2_27))
=> p__01(s__02(cbool__00,V_27t1_27)) )
=> s__02(cbool__00,V_27t1_27) = s__02(cbool__00,V_27t2_27) ) ) ).
fof('thm.bool.FALSITY',axiom,
! [V_27t_27] :
( p__01(s__02(cbool__00,cF__00))
=> p__01(s__02(cbool__00,V_27t_27)) ) ).
fof('thm.bool.EXCLUDED_MIDDLE',axiom,
! [V_27t_27] :
( p__01(s__02(cbool__00,V_27t_27))
| ~ p__01(s__02(cbool__00,V_27t_27)) ) ).
fof('thm.bool.EQ_SYM_EQ',axiom,
! [V_27A_27,V_27x_27,V_27y_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27y_27)
<=> s__02(V_27A_27,V_27y_27) = s__02(V_27A_27,V_27x_27) ) ).
fof('thm.bool.EQ_CLAUSES',axiom,
! [V_27t_27] :
( ( s__02(cbool__00,cT__00) = s__02(cbool__00,V_27t_27)
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( s__02(cbool__00,V_27t_27) = s__02(cbool__00,cT__00)
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( s__02(cbool__00,cF__00) = s__02(cbool__00,V_27t_27)
<=> ~ p__01(s__02(cbool__00,V_27t_27)) )
& ( s__02(cbool__00,V_27t_27) = s__02(cbool__00,cF__00)
<=> ~ p__01(s__02(cbool__00,V_27t_27)) ) ) ).
fof('thm.bool.COND_CLAUSES',axiom,
! [V_27A_27,V_27t1_27,V_27t2_27] :
( s__02(V_27A_27,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,cT__00),s__02(V_27A_27,V_27t1_27),s__02(V_27A_27,V_27t2_27))) = s__02(V_27A_27,V_27t1_27)
& s__02(V_27A_27,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,cF__00),s__02(V_27A_27,V_27t1_27),s__02(V_27A_27,V_27t2_27))) = s__02(V_27A_27,V_27t2_27) ) ).
fof('thm.bool.AND_IMP_INTRO',axiom,
! [V_27t1_27,V_27t2_27,V_27t3_27] :
( ( p__01(s__02(cbool__00,V_27t1_27))
=> ( p__01(s__02(cbool__00,V_27t2_27))
=> p__01(s__02(cbool__00,V_27t3_27)) ) )
<=> ( ( p__01(s__02(cbool__00,V_27t1_27))
& p__01(s__02(cbool__00,V_27t2_27)) )
=> p__01(s__02(cbool__00,V_27t3_27)) ) ) ).
fof('thm.bool.IMP_CONG',axiom,
! [V_27x_27,V_27x_7c39_7c_27,V_27y_27,V_27y_7c39_7c_27] :
( ( s__02(cbool__00,V_27x_27) = s__02(cbool__00,V_27x_7c39_7c_27)
& ( p__01(s__02(cbool__00,V_27x_7c39_7c_27))
=> s__02(cbool__00,V_27y_27) = s__02(cbool__00,V_27y_7c39_7c_27) ) )
=> ( ( p__01(s__02(cbool__00,V_27x_27))
=> p__01(s__02(cbool__00,V_27y_27)) )
<=> ( p__01(s__02(cbool__00,V_27x_7c39_7c_27))
=> p__01(s__02(cbool__00,V_27y_7c39_7c_27)) ) ) ) ).
fof('thm.pair.pair_case_thm',axiom,
! [V_27A_27,V_27B_27,V_27C_27,V_27y_27,V_27x_27,V_27f_27] : s__02(V_27A_27,c_27const_2epair_2epair__CASE_27__02(s__02(c_27type_2epair_2eprod_27__02(V_27B_27,V_27C_27),c_27const_2epair_2e_2c_27__02(s__02(V_27B_27,V_27x_27),s__02(V_27C_27,V_27y_27))),s__02(cfun__02(V_27B_27,cfun__02(V_27C_27,V_27A_27)),V_27f_27))) = s__02(V_27A_27,chapp__02(s__02(cfun__02(V_27C_27,V_27A_27),chapp__02(s__02(cfun__02(V_27B_27,cfun__02(V_27C_27,V_27A_27)),V_27f_27),s__02(V_27B_27,V_27x_27))),s__02(V_27C_27,V_27y_27))) ).
fof('thm.list.EL_LUPDATE',axiom,
! [V_27A_27,V_27ys_27,V_27x_27,V_27i_27,V_27k_27] :
? [Vv] :
( ( p__01(s__02(cbool__00,Vv))
<=> ( s__02(c_27type_2enum_2enum_27__00,V_27i_27) = s__02(c_27type_2enum_2enum_27__00,V_27k_27)
& p__01(s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27k_27),s__02(c_27type_2enum_2enum_27__00,c_27const_2elist_2eLENGTH_27__01(s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27ys_27)))))) ) )
& s__02(V_27A_27,c_27const_2elist_2eEL_27__02(s__02(c_27type_2enum_2enum_27__00,V_27i_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eLUPDATE_27__03(s__02(V_27A_27,V_27x_27),s__02(c_27type_2enum_2enum_27__00,V_27k_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27ys_27))))) = s__02(V_27A_27,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,Vv),s__02(V_27A_27,V_27x_27),s__02(V_27A_27,c_27const_2elist_2eEL_27__02(s__02(c_27type_2enum_2enum_27__00,V_27i_27),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27ys_27))))) ) ).
fof('thm.reg_alloc.tag_case_def',axiom,
! [V_27A_27] :
( ! [V_27a_27,V_27f_27,V_27v_27,V_27v1_27] : s__02(V_27A_27,c_27const_2ereg__alloc_2etag__CASE_27__04(s__02(c_27type_2ereg__alloc_2etag_27__00,c_27const_2ereg__alloc_2eFixed_27__01(s__02(c_27type_2enum_2enum_27__00,V_27a_27))),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f_27),s__02(V_27A_27,V_27v_27),s__02(V_27A_27,V_27v1_27))) = s__02(V_27A_27,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f_27),s__02(c_27type_2enum_2enum_27__00,V_27a_27)))
& ! [V_27f_27,V_27v_27,V_27v1_27] : s__02(V_27A_27,c_27const_2ereg__alloc_2etag__CASE_27__04(s__02(c_27type_2ereg__alloc_2etag_27__00,c_27const_2ereg__alloc_2eAtemp_27__00),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f_27),s__02(V_27A_27,V_27v_27),s__02(V_27A_27,V_27v1_27))) = s__02(V_27A_27,V_27v_27)
& ! [V_27f_27,V_27v_27,V_27v1_27] : s__02(V_27A_27,c_27const_2ereg__alloc_2etag__CASE_27__04(s__02(c_27type_2ereg__alloc_2etag_27__00,c_27const_2ereg__alloc_2eStemp_27__00),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f_27),s__02(V_27A_27,V_27v_27),s__02(V_27A_27,V_27v1_27))) = s__02(V_27A_27,V_27v1_27) ) ).
fof('thm.reg_alloc.tag_nchotomy',axiom,
! [V_27tt_27] :
( ? [V_27n_27] : s__02(c_27type_2ereg__alloc_2etag_27__00,V_27tt_27) = s__02(c_27type_2ereg__alloc_2etag_27__00,c_27const_2ereg__alloc_2eFixed_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27)))
| s__02(c_27type_2ereg__alloc_2etag_27__00,V_27tt_27) = s__02(c_27type_2ereg__alloc_2etag_27__00,c_27const_2ereg__alloc_2eAtemp_27__00)
| s__02(c_27type_2ereg__alloc_2etag_27__00,V_27tt_27) = s__02(c_27type_2ereg__alloc_2etag_27__00,c_27const_2ereg__alloc_2eStemp_27__00) ) ).
fof('thm.reg_allocProof.no_clash_def',axiom,
! [V__3] :
( ! [V_27n_27,V_27x_27,V_27y_27,V_27m_27] :
( p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)))),V__3),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,V_27y_27))),s__02(c_27type_2enum_2enum_27__00,V_27m_27))))
<=> ( s__02(c_27type_2enum_2enum_27__00,V_27n_27) = s__02(c_27type_2enum_2enum_27__00,V_27m_27)
=> s__02(c_27type_2enum_2enum_27__00,V_27x_27) = s__02(c_27type_2enum_2enum_27__00,V_27y_27) ) )
=> ! [V__2] :
( ! [V_27v3_27,V_27x_27,V_27y_27,V_27n_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00))),chapp__02(s__02(cfun__02(c_27type_2ereg__alloc_2etag_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)))),V__2),s__02(c_27type_2ereg__alloc_2etag_27__00,V_27v3_27))),s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,V_27y_27))),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) = s__02(cbool__00,c_27const_2ereg__alloc_2etag__CASE_27__04(s__02(c_27type_2ereg__alloc_2etag_27__00,V_27v3_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)))),V__3),s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,V_27y_27))),s__02(cbool__00,cT__00),s__02(cbool__00,cT__00)))
=> ! [V__1] :
( ! [V_27v2_27,V_27x_27,V_27y_27,V_27v3_27] : s__02(cbool__00,chapp__02(s__02(cfun__02(c_27type_2ereg__alloc_2etag_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2ereg__alloc_2etag_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2ereg__alloc_2etag_27__00,cbool__00))),chapp__02(s__02(cfun__02(c_27type_2ereg__alloc_2etag_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2ereg__alloc_2etag_27__00,cbool__00)))),V__1),s__02(c_27type_2ereg__alloc_2etag_27__00,V_27v2_27))),s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,V_27y_27))),s__02(c_27type_2ereg__alloc_2etag_27__00,V_27v3_27))) = s__02(cbool__00,c_27const_2ereg__alloc_2etag__CASE_27__04(s__02(c_27type_2ereg__alloc_2etag_27__00,V_27v2_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00))),chapp__02(s__02(cfun__02(c_27type_2ereg__alloc_2etag_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)))),V__2),s__02(c_27type_2ereg__alloc_2etag_27__00,V_27v3_27))),s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,V_27y_27))),s__02(cbool__00,cT__00),s__02(cbool__00,cT__00)))
=> ! [V__0] :
( ! [V_27x_27,V_27y_27,V_27v2_27] : s__02(cfun__02(c_27type_2ereg__alloc_2etag_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2ereg__alloc_2etag_27__00,cfun__02(c_27type_2ereg__alloc_2etag_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2ereg__alloc_2etag_27__00,cfun__02(c_27type_2ereg__alloc_2etag_27__00,cbool__00))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2ereg__alloc_2etag_27__00,cfun__02(c_27type_2ereg__alloc_2etag_27__00,cbool__00)))),V__0),s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,V_27y_27))),s__02(c_27type_2ereg__alloc_2etag_27__00,V_27v2_27))) = s__02(cfun__02(c_27type_2ereg__alloc_2etag_27__00,cbool__00),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2ereg__alloc_2etag_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2ereg__alloc_2etag_27__00,cbool__00))),chapp__02(s__02(cfun__02(c_27type_2ereg__alloc_2etag_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2ereg__alloc_2etag_27__00,cbool__00)))),V__1),s__02(c_27type_2ereg__alloc_2etag_27__00,V_27v2_27))),s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,V_27y_27)))
=> ! [V_27adj__ls_27,V_27node__tag_27] :
( p__01(s__02(cbool__00,c_27const_2ereg__allocProof_2eno__clash_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2enum_2enum_27__00)),V_27adj__ls_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2ereg__alloc_2etag_27__00),V_27node__tag_27))))
<=> ! [V_27x_27,V_27y_27] :
( p__01(s__02(cbool__00,c_27const_2ereg__allocProof_2ehas__edge_27__03(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2enum_2enum_27__00)),V_27adj__ls_27),s__02(c_27type_2enum_2enum_27__00,V_27x_27),s__02(c_27type_2enum_2enum_27__00,V_27y_27))))
=> p__01(s__02(cbool__00,c_27const_2epair_2epair__CASE_27__02(s__02(c_27type_2epair_2eprod_27__02(c_27type_2ereg__alloc_2etag_27__00,c_27type_2ereg__alloc_2etag_27__00),c_27const_2epair_2e_2c_27__02(s__02(c_27type_2ereg__alloc_2etag_27__00,c_27const_2elist_2eEL_27__02(s__02(c_27type_2enum_2enum_27__00,V_27x_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2ereg__alloc_2etag_27__00),V_27node__tag_27))),s__02(c_27type_2ereg__alloc_2etag_27__00,c_27const_2elist_2eEL_27__02(s__02(c_27type_2enum_2enum_27__00,V_27y_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2ereg__alloc_2etag_27__00),V_27node__tag_27))))),s__02(cfun__02(c_27type_2ereg__alloc_2etag_27__00,cfun__02(c_27type_2ereg__alloc_2etag_27__00,cbool__00)),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2ereg__alloc_2etag_27__00,cfun__02(c_27type_2ereg__alloc_2etag_27__00,cbool__00))),chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2ereg__alloc_2etag_27__00,cfun__02(c_27type_2ereg__alloc_2etag_27__00,cbool__00)))),V__0),s__02(c_27type_2enum_2enum_27__00,V_27x_27))),s__02(c_27type_2enum_2enum_27__00,V_27y_27)))))) ) ) ) ) ) ) ).
fof(conjecture,conjecture,
! [V_27adjls_27,V_27tags_27,V_27n_27] :
( p__01(s__02(cbool__00,c_27const_2ereg__allocProof_2eno__clash_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2enum_2enum_27__00)),V_27adjls_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2ereg__alloc_2etag_27__00),V_27tags_27))))
=> p__01(s__02(cbool__00,c_27const_2ereg__allocProof_2eno__clash_27__02(s__02(c_27type_2elist_2elist_27__01(c_27type_2elist_2elist_27__01(c_27type_2enum_2enum_27__00)),V_27adjls_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2ereg__alloc_2etag_27__00),c_27const_2elist_2eLUPDATE_27__03(s__02(c_27type_2ereg__alloc_2etag_27__00,c_27const_2ereg__alloc_2eStemp_27__00),s__02(c_27type_2enum_2enum_27__00,V_27n_27),s__02(c_27type_2elist_2elist_27__01(c_27type_2ereg__alloc_2etag_27__00),V_27tags_27)))))) ) ).
%------------------------------------------------------------------------------