TPTP Problem File: SWW908+1.p
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%------------------------------------------------------------------------------
% File : SWW908+1 : TPTP v8.2.0. Released v7.3.0.
% Domain : Software Verification
% Problem : word_to_stackProof__52__tactictoe_prove_51__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : word_to_stackProof__52__tactictoe_prove_51__dep [Kum18]
% Status : CounterSatisfiable
% Rating : 0.00 v8.1.0, 0.25 v7.5.0, 0.60 v7.4.0, 0.00 v7.3.0
% Syntax : Number of formulae : 26 ( 6 unt; 0 def)
% Number of atoms : 105 ( 33 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 84 ( 5 ~; 1 |; 27 &)
% ( 24 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 20 ( 20 usr; 5 con; 0-3 aty)
% Number of variables : 85 ( 83 !; 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.FORALL_SIMP',axiom,
! [V_27A_27,V_27t_27] :
( ! [V_27x_27] : p__01(s__02(cbool__00,V_27t_27))
<=> p__01(s__02(cbool__00,V_27t_27)) ) ).
fof('thm.bool.AND_CLAUSES',axiom,
! [V_27t_27] :
( ( ( p__01(s__02(cbool__00,cT__00))
& p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
& p__01(s__02(cbool__00,cT__00)) )
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ( p__01(s__02(cbool__00,cF__00))
& p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,cF__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
& p__01(s__02(cbool__00,cF__00)) )
<=> p__01(s__02(cbool__00,cF__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
& p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,V_27t_27)) ) ) ).
fof('thm.bool.IMP_CLAUSES',axiom,
! [V_27t_27] :
( ( ( p__01(s__02(cbool__00,cT__00))
=> p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,V_27t_27)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
=> p__01(s__02(cbool__00,cT__00)) )
<=> p__01(s__02(cbool__00,cT__00)) )
& ( ( p__01(s__02(cbool__00,cF__00))
=> p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,cT__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
=> p__01(s__02(cbool__00,V_27t_27)) )
<=> p__01(s__02(cbool__00,cT__00)) )
& ( ( p__01(s__02(cbool__00,V_27t_27))
=> p__01(s__02(cbool__00,cF__00)) )
<=> ~ p__01(s__02(cbool__00,V_27t_27)) ) ) ).
fof('thm.bool.REFL_CLAUSE',axiom,
! [V_27A_27,V_27x_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27x_27)
<=> p__01(s__02(cbool__00,cT__00)) ) ).
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.FUN_EQ_THM',axiom,
! [V_27B_27,V_27A_27,V_27f_27,V_27g_27] :
( s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27) = s__02(cfun__02(V_27A_27,V_27B_27),V_27g_27)
<=> ! [V_27x_27] : s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,V_27x_27))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27g_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.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.bool.COND_CONG',axiom,
! [V_27A_27,V_27P_27,V_27Q_27,V_27x_27,V_27x_7c39_7c_27,V_27y_27,V_27y_7c39_7c_27] :
( ( s__02(cbool__00,V_27P_27) = s__02(cbool__00,V_27Q_27)
& ( p__01(s__02(cbool__00,V_27Q_27))
=> s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27x_7c39_7c_27) )
& ( ~ p__01(s__02(cbool__00,V_27Q_27))
=> s__02(V_27A_27,V_27y_27) = s__02(V_27A_27,V_27y_7c39_7c_27) ) )
=> s__02(V_27A_27,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,V_27P_27),s__02(V_27A_27,V_27x_27),s__02(V_27A_27,V_27y_27))) = s__02(V_27A_27,c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,V_27Q_27),s__02(V_27A_27,V_27x_7c39_7c_27),s__02(V_27A_27,V_27y_7c39_7c_27))) ) ).
fof('thm.bool.UNWIND_THM2',axiom,
! [V_27A_27,V_27P_27,V_27a_27] :
( ? [V_27x_27] :
( s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27a_27)
& p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(V_27A_27,V_27x_27)))) )
<=> p__01(s__02(cbool__00,chapp__02(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27),s__02(V_27A_27,V_27a_27)))) ) ).
fof('thm.bool.bool_case_thm',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)
& ! [V_27t1_27,V_27t2_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.combin.I_THM',axiom,
! [V_27A_27,V_27x_27] : s__02(V_27A_27,chapp__02(s__02(cfun__02(V_27A_27,V_27A_27),c_27const_2ecombin_2eI_27__00),s__02(V_27A_27,V_27x_27))) = s__02(V_27A_27,V_27x_27) ).
fof('thm.pred_set.INJ_DEF',axiom,
! [V_27B_27,V_27A_27,V_27f_27,V_27s_27,V_27t_27] :
( p__01(s__02(cbool__00,c_27const_2epred__set_2eINJ_27__03(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(cfun__02(V_27A_27,cbool__00),V_27s_27),s__02(cfun__02(V_27B_27,cbool__00),V_27t_27))))
<=> ( ! [V_27x_27] :
( p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27A_27,V_27x_27),s__02(cfun__02(V_27A_27,cbool__00),V_27s_27))))
=> p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,V_27x_27))),s__02(cfun__02(V_27B_27,cbool__00),V_27t_27)))) )
& ! [V_27x_27,V_27y_27] :
( ( p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27A_27,V_27x_27),s__02(cfun__02(V_27A_27,cbool__00),V_27s_27))))
& p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27A_27,V_27y_27),s__02(cfun__02(V_27A_27,cbool__00),V_27s_27)))) )
=> ( s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,V_27x_27))) = s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,V_27y_27)))
=> s__02(V_27A_27,V_27x_27) = s__02(V_27A_27,V_27y_27) ) ) ) ) ).
fof('thm.pred_set.SURJ_DEF',axiom,
! [V_27A_27,V_27B_27,V_27f_27,V_27s_27,V_27t_27] :
( p__01(s__02(cbool__00,c_27const_2epred__set_2eSURJ_27__03(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(cfun__02(V_27A_27,cbool__00),V_27s_27),s__02(cfun__02(V_27B_27,cbool__00),V_27t_27))))
<=> ( ! [V_27x_27] :
( p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27A_27,V_27x_27),s__02(cfun__02(V_27A_27,cbool__00),V_27s_27))))
=> p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,V_27x_27))),s__02(cfun__02(V_27B_27,cbool__00),V_27t_27)))) )
& ! [V_27x_27] :
( p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27B_27,V_27x_27),s__02(cfun__02(V_27B_27,cbool__00),V_27t_27))))
=> ? [V_27y_27] :
( p__01(s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(V_27A_27,V_27y_27),s__02(cfun__02(V_27A_27,cbool__00),V_27s_27))))
& s__02(V_27B_27,chapp__02(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(V_27A_27,V_27y_27))) = s__02(V_27B_27,V_27x_27) ) ) ) ) ).
fof('thm.pred_set.BIJ_DEF',axiom,
! [V_27A_27,V_27B_27,V_27f_27,V_27s_27,V_27t_27] :
( p__01(s__02(cbool__00,c_27const_2epred__set_2eBIJ_27__03(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(cfun__02(V_27A_27,cbool__00),V_27s_27),s__02(cfun__02(V_27B_27,cbool__00),V_27t_27))))
<=> ( p__01(s__02(cbool__00,c_27const_2epred__set_2eINJ_27__03(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(cfun__02(V_27A_27,cbool__00),V_27s_27),s__02(cfun__02(V_27B_27,cbool__00),V_27t_27))))
& p__01(s__02(cbool__00,c_27const_2epred__set_2eSURJ_27__03(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(cfun__02(V_27A_27,cbool__00),V_27s_27),s__02(cfun__02(V_27B_27,cbool__00),V_27t_27)))) ) ) ).
fof('thm.pred_set.IN_COUNT',axiom,
! [V_27m_27,V_27n_27] : s__02(cbool__00,c_27const_2ebool_2eIN_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2epred__set_2ecount_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))))) = s__02(cbool__00,c_27const_2eprim__rec_2e_3c_27__02(s__02(c_27type_2enum_2enum_27__00,V_27m_27),s__02(c_27type_2enum_2enum_27__00,V_27n_27))) ).
fof('thm.misc.GENLIST_ID',axiom,
! [V_27A_27,V__0] :
( ! [V_27x_27,V_27i_27] : s__02(V_27A_27,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cfun__02(c_27type_2enum_2enum_27__00,V_27A_27)),V__0),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27x_27))),s__02(c_27type_2enum_2enum_27__00,V_27i_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_27x_27)))
=> ! [V_27x_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eGENLIST_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cfun__02(c_27type_2enum_2enum_27__00,V_27A_27)),V__0),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27x_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_27x_27))))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27x_27) ) ).
fof('thm.wordSem.list_rearrange_def',axiom,
! [V_27A_27,V__0] :
( ! [V_27mover_27,V_27xs_27,V_27i_27] : s__02(V_27A_27,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cfun__02(c_27type_2enum_2enum_27__00,V_27A_27)),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cfun__02(c_27type_2enum_2enum_27__00,V_27A_27))),V__0),s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27mover_27))),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27xs_27))),s__02(c_27type_2enum_2enum_27__00,V_27i_27))) = s__02(V_27A_27,c_27const_2elist_2eEL_27__02(s__02(c_27type_2enum_2enum_27__00,chapp__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27mover_27),s__02(c_27type_2enum_2enum_27__00,V_27i_27))),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27xs_27)))
=> ! [V_27mover_27,V_27xs_27] : s__02(c_27type_2elist_2elist_27__01(V_27A_27),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27type_2elist_2elist_27__01(V_27A_27)),c_27const_2ewordSem_2elist__rearrange_27__01(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27mover_27))),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27xs_27))) = s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2ebool_2eCOND_27__03(s__02(cbool__00,c_27const_2epred__set_2eBIJ_27__03(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27mover_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2epred__set_2ecount_27__01(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_27xs_27))))),s__02(cfun__02(c_27type_2enum_2enum_27__00,cbool__00),c_27const_2epred__set_2ecount_27__01(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_27xs_27))))))),s__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27const_2elist_2eGENLIST_27__02(s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),chapp__02(s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cfun__02(c_27type_2enum_2enum_27__00,V_27A_27)),chapp__02(s__02(cfun__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),cfun__02(c_27type_2enum_2enum_27__00,V_27A_27))),V__0),s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),V_27mover_27))),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27xs_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_27xs_27))))),s__02(c_27type_2elist_2elist_27__01(V_27A_27),V_27xs_27))) ) ).
fof(conjecture,conjecture,
! [V_27A_27] : s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27type_2elist_2elist_27__01(V_27A_27)),c_27const_2ewordSem_2elist__rearrange_27__01(s__02(cfun__02(c_27type_2enum_2enum_27__00,c_27type_2enum_2enum_27__00),c_27const_2ecombin_2eI_27__00))) = s__02(cfun__02(c_27type_2elist_2elist_27__01(V_27A_27),c_27type_2elist_2elist_27__01(V_27A_27)),c_27const_2ecombin_2eI_27__00) ).
%------------------------------------------------------------------------------