TPTP Problem File: SWW899+1.p
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%------------------------------------------------------------------------------
% File : SWW899+1 : TPTP v9.0.0. Released v7.3.0.
% Domain : Software Verification
% Problem : exh_to_patProof__22__bind_mono__dep
% Version : Especial.
% English :
% Refs : [Kum18] Kumar (2018), Email to Geoff Sutcliffe
% Source : [Kum18]
% Names : exh_to_patProof__22__bind_mono__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 : 18 ( 6 unt; 0 def)
% Number of atoms : 61 ( 20 equ)
% Maximal formula atoms : 15 ( 3 avg)
% Number of connectives : 47 ( 4 ~; 2 |; 10 &)
% ( 12 <=>; 19 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 10 ( 2 avg)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 20 ( 20 usr; 6 con; 0-3 aty)
% Number of variables : 50 ( 49 !; 1 ?)
% 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.SELECT_AX',axiom,
! [V_27A_27,V_27P_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_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,c_27const_2emin_2e_40_27__01(s__02(cfun__02(V_27A_27,cbool__00),V_27P_27)))))) ) ).
fof('thm.bool.TRUTH',axiom,
p__01(s__02(cbool__00,cT__00)) ).
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.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.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.combin.I_THM',axiom,
! [V_27A_27,V_27x_27] : s__02(V_27A_27,c_27const_2ecombin_2eI_27__01(s__02(V_27A_27,V_27x_27))) = s__02(V_27A_27,V_27x_27) ).
fof('thm.relation.WF_EMPTY_REL',axiom,
! [V_27A_27] : p__01(s__02(cbool__00,c_27const_2erelation_2eWF_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),c_27const_2erelation_2eEMPTY__REL_27__00)))) ).
fof('thm.relation.WFREC_COROLLARY',axiom,
! [V_27B_27,V_27A_27,V_27M_27,V_27R_27,V_27f_27] :
( s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27) = s__02(cfun__02(V_27A_27,V_27B_27),c_27const_2erelation_2eWFREC_27__02(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R_27),s__02(cfun__02(cfun__02(V_27A_27,V_27B_27),cfun__02(V_27A_27,V_27B_27)),V_27M_27)))
=> ( p__01(s__02(cbool__00,c_27const_2erelation_2eWF_27__01(s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R_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),chapp__02(s__02(cfun__02(cfun__02(V_27A_27,V_27B_27),cfun__02(V_27A_27,V_27B_27)),V_27M_27),s__02(cfun__02(V_27A_27,V_27B_27),c_27const_2erelation_2eRESTRICT_27__03(s__02(cfun__02(V_27A_27,V_27B_27),V_27f_27),s__02(cfun__02(V_27A_27,cfun__02(V_27A_27,cbool__00)),V_27R_27),s__02(V_27A_27,V_27x_27))))),s__02(V_27A_27,V_27x_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.arithmetic.num_case_def',axiom,
! [V_27A_27] :
( ! [V_27v_27,V_27f_27] : s__02(V_27A_27,c_27const_2earithmetic_2enum__CASE_27__03(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00),s__02(V_27A_27,V_27v_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)
& ! [V_27n_27,V_27v_27,V_27f_27] : s__02(V_27A_27,c_27const_2earithmetic_2enum__CASE_27__03(s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))),s__02(V_27A_27,V_27v_27),s__02(cfun__02(c_27type_2enum_2enum_27__00,V_27A_27),V_27f_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_27n_27))) ) ).
fof('thm.arithmetic.num_CASES',axiom,
! [V_27m_27] :
( s__02(c_27type_2enum_2enum_27__00,V_27m_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2e0_27__00)
| ? [V_27n_27] : s__02(c_27type_2enum_2enum_27__00,V_27m_27) = s__02(c_27type_2enum_2enum_27__00,c_27const_2enum_2eSUC_27__01(s__02(c_27type_2enum_2enum_27__00,V_27n_27))) ) ).
fof(conjecture,conjecture,
! [V_27V1_27,V_27V2_27,V_27x_27,V_27y_27] :
( ! [V_27x0_27,V_27y0_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)),V_27V1_27),s__02(c_27type_2enum_2enum_27__00,V_27x0_27))),s__02(c_27type_2enum_2enum_27__00,V_27y0_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)),V_27V2_27),s__02(c_27type_2enum_2enum_27__00,V_27x0_27))),s__02(c_27type_2enum_2enum_27__00,V_27y0_27)))) )
=> ( p__01(s__02(cbool__00,c_27const_2eexh__to__patProof_2ebind_27__03(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__00)),V_27V1_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_2eexh__to__patProof_2ebind_27__03(s__02(cfun__02(c_27type_2enum_2enum_27__00,cfun__02(c_27type_2enum_2enum_27__00,cbool__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)))) ) ) ).
%------------------------------------------------------------------------------